Dr Chris Goodrich

Phone

9385 7036

E-mail

c.goodrich@unsw.edu.au

Location

School of Mathematics and Statistics UNSW Sydney NSW 2052 The Red Centre Room 2070

Books | 2016

Goodrich C; Peterson AC, 2016, Discrete fractional calculus,
Journal articles | 2024

Goodrich CS, 2024, 'A surprising property of nonlocal operators: The deregularising effect of nonlocal elements in convolution differential equations', Advanced Nonlinear Studies,

Journal articles | 2024

Goodrich CS, 2024, 'A unified characterization of convolution coefficients in nonlocal differential equations', Proceedings of the Royal Society of Edinburgh Section A: Mathematics,

Journal articles | 2024

Goodrich CS, 2024, 'An application of Sobolev's inequality to one-dimensional Kirchhoff equations', Journal of Differential Equations, 385, pp. 463 - 486,

Journal articles | 2024

Goodrich CS, 2024, 'NONEXISTENCE OF NONTRIVIAL SOLUTIONS TO KIRCHHOFF-LIKE EQUATIONS', Proceedings of the American Mathematical Society, Series B, 11, pp. 304 - 314,

Journal articles | 2023

Ali MA; Goodrich CS; Budak H, 2023, 'Some new parameterized Newton-type inequalities for differentiable functions via fractional integrals', Journal of Inequalities and Applications, 2023,

Journal articles | 2023

Ali MA; Goodrich CS, 2023, 'On some new inequalities of Hermite-Hadamard-Mercer midpoint and trapezoidal type in q-calculus', Analysis (Germany),

Journal articles | 2023

Goodrich CS, 2023, 'Convolution equations with variable time nonlocal coefficients', Applied Mathematics Letters, 145,

Journal articles | 2023

Goodrich CS, 2023, 'Nonlocal differential equations with convex convolution coefficients', Journal of Fixed Point Theory and Applications, 25,

Journal articles | 2023

Goodrich CS, 2023, 'Nonlocal differential equations with (p,q) growth', Bulletin of the London Mathematical Society, 55, pp. 1373 - 1391,

Journal articles | 2023

Mohammed PO; Dahal R; Goodrich CS; Hamed YS; Baleanu D, 2023, 'Analytical and numerical negative boundedness of fractional differences with Mittag–Leffler kernel', AIMS Mathematics, 8, pp. 5540 - 5550,

Journal articles | 2023

Mohammed PO; Goodrich CS; Srivastava HM; Al-Sarairah E; Hamed YS, 2023, 'A Study of Monotonicity Analysis for the Delta and Nabla Discrete Fractional Operators of the Liouville–Caputo Family', Axioms, 12,

Journal articles | 2022

Goodrich C; Lizama C, 2022, 'Existence and monotonicity of nonlocal boundary value problems: The one-dimensional case', Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 152, pp. 1 - 27,

Journal articles | 2022

Goodrich C; Scilla G; Stroffolini B, 2022, 'Partial regularity for minimizers of discontinuous quasiconvex integrals with general growth', Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 152, pp. 1191 - 1232,

Journal articles | 2022

Goodrich CS; Scapellato A, 2022, 'Partial regularity of minimizers of asymptotically convex functionals with p(x)-growth', STUDIA MATHEMATICA,

Journal articles | 2022

Goodrich CS; Scapellato A, 2022, 'Partial regularity of minimizers of asymptotically convex functionals with p(x)-growth', Studia Mathematica, 264, pp. 71 - 102,

Journal articles | 2022

Goodrich CS, 2022, 'An analysis of nonlocal difference equations with finite convolution coefficients', Journal of Fixed Point Theory and Applications, 24,

Journal articles | 2022

Goodrich CS, 2022, 'NONEXISTENCE AND PARAMETER RANGE ESTIMATES FOR CONVOLUTION DIFFERENTIAL EQUATIONS', Proceedings of the American Mathematical Society, Series B, 9, pp. 254 - 265,

Journal articles | 2022

Mohammed PO; Goodrich CS; Brzo AB; Baleanu D; Hamed YS, 2022, 'New classifications of monotonicity investigation for discrete operators with Mittag-Leffler kernel', Mathematical Biosciences and Engineering, 19, pp. 4062 - 4074,

Journal articles | 2022

Mohammed PO; Goodrich CS; Hamasalh FK; Kashuri A; Hamed YS, 2022, 'On positivity and monotonicity analysis for discrete fractional operators with discrete Mittag–Leffler kernel', Mathematical Methods in the Applied Sciences, 45, pp. 6391 - 6410,

Journal articles | 2021

Dahal R; GOODRICH CS, 2021, 'ANALYSIS OF CONVEXITY RESULTS FOR DISCRETE FRACTIONAL NABLA OPERATORS', Rocky Mountain Journal of Mathematics, 51, pp. 1981 - 2001,

Journal articles | 2021

Dahal R; Goodrich CS; Lyons B, 2021, 'Monotonicity results for sequential fractional differences of mixed orders with negative lower bound', Journal of Difference Equations and Applications, 27, pp. 1574 - 1593,

Journal articles | 2021

Dahal R; Goodrich CS, 2021, 'Theoretical and numerical analysis of monotonicity results for fractional difference operators', Applied Mathematics Letters, 117,

Journal articles | 2021

Goodrich CS; Jonnalagadda JM; Lyons B, 2021, 'Convexity, monotonicity, and positivity results for sequential fractional nabla difference operators with discrete exponential kernels', Mathematical Methods in the Applied Sciences, 44, pp. 7099 - 7120,

Journal articles | 2021

Goodrich CS; Jonnalagadda JM, 2021, 'An analysis of polynomial sequences and their application to discrete fractional operators', Journal of Difference Equations and Applications, 27, pp. 1081 - 1102,

Journal articles | 2021

Goodrich CS; Jonnalagadda JM, 2021, 'Monotonicity results for CFC nabla fractional differences with negative lower bound', Analysis (Germany), 41, pp. 221 - 229,

Journal articles | 2021

Goodrich CS; Lyons B; Scapellato A; Velcsov MT, 2021, 'Analytical and numerical convexity results for discrete fractional sequential differences with negative lower bound', Journal of Difference Equations and Applications, 27, pp. 317 - 341,

Journal articles | 2021

Goodrich CS; Lyons B; Velcsov MT, 2021, 'ANALYTICAL and NUMERICAL MONOTONICITY RESULTS for DISCRETE FRACTIONAL SEQUENTIAL DIFFERENCES with NEGATIVE LOWER BOUND', Communications on Pure and Applied Analysis, 20, pp. 339 - 358,

Journal articles | 2021

Goodrich CS, 2021, 'A TOPOLOGICAL APPROACH TO A CLASS OF ONE-DIMENSIONAL KIRCHHOFF EQUATIONS', Proceedings of the American Mathematical Society, Series B, 8, pp. 158 - 172,

Journal articles | 2021

Goodrich CS, 2021, 'A one-dimensional Kirchhoff equation with generalized convolution coefficients', Journal of Fixed Point Theory and Applications, 23,

Journal articles | 2021

Goodrich CS, 2021, 'A topological approach to nonlocal elliptic partial differential equations on an annulus', Mathematische Nachrichten, 294, pp. 286 - 309,

Journal articles | 2021

Goodrich CS, 2021, 'Differential equations with multiple sign changing convolution coefficients', International Journal of Mathematics, 32,

Journal articles | 2021

Goodrich CS, 2021, 'Discrete Kirchhoff equations with sign-changing coefficients', Journal of Difference Equations and Applications, 27, pp. 664 - 685,

Journal articles | 2021

Goodrich CS, 2021, 'Nonlocal Differential Equations with Convolution Coefficients and Applications to Fractional Calculus', Advanced Nonlinear Studies, 21, pp. 767 - 787,

Journal articles | 2021

Goodrich CS, 2021, 'Nonlocal differential equations with concave coefficients of convolution type', Nonlinear Analysis, Theory, Methods and Applications, 211,

Journal articles | 2021

Goodrich CS, 2021, 'Partial regularity of minimizers of asymptotically convex functionals with Morrey coefficients', Journal of Mathematical Analysis and Applications, 498,

Journal articles | 2021

Goodrich CS, 2021, 'Topological analysis of doubly nonlocal boundary value problems', Journal of Fixed Point Theory and Applications, 23,

Journal articles | 2020

Goodrich C; Lizama C, 2020, 'A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity', Israel Journal of Mathematics, 236, pp. 533 - 589,

Journal articles | 2020

Goodrich C; Lizama C, 2020, 'Positivity, monotonicity, and convexity for convolution operators', Discrete and Continuous Dynamical Systems- Series A, 40, pp. 4961 - 4983,

Journal articles | 2020

Goodrich CS; Lyons B, 2020, 'Nonlocal difference equations with sign-changing coefficients', Applied Mathematics Letters, 106,

Journal articles | 2020

Goodrich CS; Lyons B, 2020, 'Positivity and monotonicity results for triple sequential fractional differences via convolution', Analysis (Germany), 40, pp. 89 - 103,

Journal articles | 2020

Goodrich CS; Ragusa MA; Scapellato A, 2020, 'Partial regularity of solutions to p(x)-Laplacian PDEs with discontinuous coefficients', Journal of Differential Equations, 268, pp. 5440 - 5468,

Journal articles | 2020

Goodrich CS, 2020, 'Pointwise conditions for perturbed Hammerstein integral equations with monotone nonlinear, nonlocal elements', Banach Journal of Mathematical Analysis, 14, pp. 290 - 312,

Journal articles | 2019

Anceschi F; Goodrich CS; Scapellato A, 2019, 'Operators with gaussian kernel bounds on mixed morrey spaces', Filomat, 33, pp. 5219 - 5230,

Journal articles | 2019

Dahal R; Goodrich CS, 2019, 'A uniformly sharp convexity result for discrete fractional sequential differences', Rocky Mountain Journal of Mathematics, 49, pp. 2571 - 2586,

Journal articles | 2019

Dahal R; Goodrich CS, 2019, 'An application of a nonstandard cone to discrete boundary value problems with unbounded indefinite forcing', Journal of Difference Equations and Applications, 25, pp. 882 - 903,

Journal articles | 2019

Dahal R; Goodrich CS, 2019, 'Mixed order monotonicity results for sequential fractional nabla differences', Journal of Difference Equations and Applications, 25, pp. 837 - 854,

Journal articles | 2019

Goodrich CS; Muellner M, 2019, 'An analysis of the sharpness of monotonicity results via homotopy for sequential fractional operators', Applied Mathematics Letters, 98, pp. 446 - 452,

Journal articles | 2019

Goodrich CS; Ragusa MA, 2019, 'Hölder continuity of weak solutions of p-Laplacian PDEs with VMO coefficients', Nonlinear Analysis, Theory, Methods and Applications, 185, pp. 336 - 355,

Journal articles | 2019

Goodrich CS, 2019, 'Coercive functionals and their relationship to multiplicity of solution to nonlocal boundary value problems', Topological Methods in Nonlinear Analysis, 54, pp. 409 - 426,

Journal articles | 2019

Goodrich CS, 2019, 'Sharp monotonicity results for fractional nabla sequential differences', Journal of Difference Equations and Applications, 25, pp. 801 - 814,

Journal articles | 2019

Xu J; Goodrich CS; Cui Y, 2019, 'Positive solutions for a system of first-order discrete fractional boundary value problems with semipositone nonlinearities', Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 113, pp. 1343 - 1358,

Journal articles | 2018

Goodrich CS, 2018, 'A general low-order partial regularity theory for asymptotically convex functionals with asymptotic dependence on the minimizer', Calculus of Variations and Partial Differential Equations, 57,

Journal articles | 2018

Goodrich CS, 2018, 'A uniformly sharp monotonicity result for discrete fractional sequential differences', Archiv der Mathematik, 110, pp. 145 - 154,

Journal articles | 2018

Goodrich CS, 2018, 'Monotonicity and non-monotonicity results for sequential fractional delta differences of mixed order', Positivity, 22, pp. 551 - 573,

Journal articles | 2018

Goodrich CS, 2018, 'New Harnack inequalities and existence theorems for radially symmetric solutions of elliptic PDEs with sign changing or vanishing Green's function', Journal of Differential Equations, 264, pp. 236 - 262,

Journal articles | 2018

Goodrich CS, 2018, 'Partial regularity of minimizers of functionals with discontinuous coefficients of low integrability with applications to nonlinear elliptic systems', Communications in Partial Differential Equations, 43, pp. 1599 - 1626,

Journal articles | 2018

Goodrich CS, 2018, 'Perturbed Integral Operator Equations of Volterra Type with Applications to p -Laplacian Equations', Mediterranean Journal of Mathematics, 15,

Journal articles | 2018

Goodrich CS, 2018, 'Radially symmetric solutions of elliptic PDEs with uniformly negative weight', Annali di Matematica Pura ed Applicata, 197, pp. 1585 - 1611,

Journal articles | 2017

Baoguo J; Erbe L; Goodrich C; Peterson A, 2017, 'The relation between nabla fractional differences and Nabla integer differences', Filomat, 31, pp. 1741 - 1753,

Journal articles | 2017

Dahal R; Drvol S; Goodrich CS, 2017, 'New monotonicity conditions in discrete fractional calculus with applications to extremality conditions', Analysis (Germany), 37, pp. 145 - 156,

Journal articles | 2017

Dahal R; Goodrich CS, 2017, 'An almost sharp monotonicity result for discrete sequential fractional delta differences', Journal of Difference Equations and Applications, 23, pp. 1190 - 1203,

Journal articles | 2017

Erbe L; Goodrich CS; Jia B; Peterson A, 2017, 'Monotonicity results for delta fractional differences revisited', Mathematica Slovaca, 67, pp. 895 - 906,

Journal articles | 2017

Goodrich CS, 2017, 'A new coercivity condition applied to semipositone integral equations with nonpositive, unbounded nonlinearities and applications to nonlocal BVPs', Journal of Fixed Point Theory and Applications, 19, pp. 1905 - 1938,

Journal articles | 2017

Goodrich CS, 2017, 'A sharp convexity result for sequential fractional delta differences', Journal of Difference Equations and Applications, 23, pp. 1986 - 2003,

Journal articles | 2017

Goodrich CS, 2017, 'Coercive nonlocal elements in fractional differential equations', Positivity, 21, pp. 377 - 394,

Journal articles | 2017

Goodrich CS, 2017, 'On Semipositone Non-Local Boundary-Value Problems with Nonlinear or Affine Boundary Conditions', Proceedings of the Edinburgh Mathematical Society, 60, pp. 635 - 649,

Journal articles | 2017

Goodrich CS, 2017, 'Partial Lipschitz regularity of minimizers of asymptotically convex functionals with general growth conditions', Journal of Differential Equations, 263, pp. 4400 - 4428,

Journal articles | 2017

Goodrich CS, 2017, 'Pointwise conditions in discrete boundary value problems with nonlocal boundary conditions', Applied Mathematics Letters, 67, pp. 7 - 15,

Journal articles | 2017

Goodrich CS, 2017, 'The effect of a nonstandard cone on existence theorem applicability in nonlocal boundary value problems', Journal of Fixed Point Theory and Applications, 19, pp. 2629 - 2646,

Journal articles | 2016

Erbe L; Goodrich CS; Jia B; Peterson A, 2016, 'Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions', Advances in Difference Equations, 2016, pp. 1 - 31,

Journal articles | 2016

Foss MD; Goodrich CS, 2016, 'On partial Hölder continuity and a Caccioppoli inequality for minimizers of asymptotically convex functionals between Riemannian manifolds', Annali di Matematica Pura ed Applicata, 195, pp. 1405 - 1461,

Journal articles | 2016

Goodrich CS, 2016, 'A note on convexity, concavity, and growth conditions in discrete fractional calculus with delta difference', Mathematical Inequalities and Applications, 19, pp. 769 - 779,

Journal articles | 2016

Goodrich CS, 2016, 'A note on perturbed Hammerstein equations with applications to nonlocal boundary value problems', Analysis (Germany), 36, pp. 183 - 193,

Journal articles | 2016

Goodrich CS, 2016, 'Coercivity of linear functionals on finite dimensional spaces and its application to discrete BVPs', Journal of Difference Equations and Applications, 22, pp. 623 - 636,

Journal articles | 2016

Goodrich CS, 2016, 'Perturbed hammerstein integral equations with sign-changing kernels and applications to nonlocal boundary value problems and elliptic pdes', Journal of Integral Equations and Applications, 28, pp. 509 - 549,

Journal articles | 2016

Goodrich CS, 2016, 'Summation equations with sign changing kernels and applications to discrete fractional boundary value problems', Commentationes Mathematicae Universitatis Carolinae, 57, pp. 201 - 229,

Journal articles | 2016

Goodrich CS, 2016, 'The relationship between sequential fractional differences and convexity', Applicable Analysis and Discrete Mathematics, 10, pp. 345 - 365,

Journal articles | 2015

Dahal R; Goodrich CS, 2015, 'Erratum to: A monotonicity result for discrete fractional difference operators[Arch. Math.(2014), 102, 293-299, DOI 10.1007/s00013-014-0620-x]', Archiv der Mathematik, 104, pp. 599 - 600,

Journal articles | 2015

Ferreira RAC; Goodrich CS, 2015, 'On positive solutions to fractional difference inclusions', Analysis (Germany), 35, pp. 73 - 83,

Journal articles | 2015

Foss M; Goodrich CS, 2015, 'Partial hölder continuity of minimizers of functionals satisfying a general asymptotic relatedness condition', Journal of Convex Analysis, 22, pp. 219 - 246

Journal articles | 2015

Goodrich CS, 2015, 'Coupled systems of boundary value problems with nonlocal boundary conditions', Applied Mathematics Letters, 41, pp. 17 - 22,

Journal articles | 2015

Goodrich CS, 2015, 'Partial Hölder continuity of minimizers of functionals satisfying a VMO condition', Advances in Calculus of Variations, 2015, pp. 83 - 110,

Journal articles | 2015

Goodrich CS, 2015, 'Semipositone boundary value problems with nonlocal, nonlinear boundary conditions', Advances in Differential Equations, 20, pp. 117 - 142

Journal articles | 2015

Goodrich CS, 2015, 'Systems of discrete fractional boundary value problems with nonlinearities satisfying no growth conditions', Journal of Difference Equations and Applications, 21, pp. 437 - 453,

Journal articles | 2014

Dahal R; Duncan D; Goodrich CS, 2014, 'Systems of semipositone discrete fractional boundary value problems', Journal of Difference Equations and Applications, 20, pp. 473 - 491,

Journal articles | 2014

Dahal R; Goodrich CS, 2014, 'A monotonicity result for discrete fractional difference operators', Archiv der Mathematik, 102, pp. 293 - 299,

Journal articles | 2014

Goodrich CS, 2014, 'A convexity result for fractional differences', Applied Mathematics Letters, 35, pp. 58 - 62,

Journal articles | 2014

Goodrich CS, 2014, 'A note on semipositone boundary value problems with nonlocal, nonlinear boundary conditions', Archiv der Mathematik, 103, pp. 177 - 187,

Journal articles | 2014

Goodrich CS, 2014, 'On Nonlinear Boundary Conditions Involving Decomposable Linear Functionals', Proceedings of the Edinburgh Mathematical Society, 58, pp. 421 - 439,

Journal articles | 2014

Goodrich CS, 2014, 'On a first-order semipositone boundary value problem on a time scale', Applicable Analysis and Discrete Mathematics, 8, pp. 269 - 287,

Journal articles | 2013

Goodrich CS, 2013, 'Existence of a positive solution to a nonlocal semipositone boundary value problem on a time scale', Commentationes Mathematicae Universitatis Carolinae, 54, pp. 509 - 525

Journal articles | 2013

Goodrich CS, 2013, 'On a Nonlocal BVP with Nonlinear Boundary Conditions', Results in Mathematics, 63, pp. 1351 - 1364,

Journal articles | 2013

Goodrich CS, 2013, 'On nonlinear boundary conditions satisfying certain asymptotic behavior', Nonlinear Analysis, Theory, Methods and Applications, 76, pp. 58 - 67,

Journal articles | 2013

Goodrich CS, 2013, 'On semipositone discrete fractional boundary value problems with non-local boundary conditions', Journal of Difference Equations and Applications, 19, pp. 1758 - 1780,

Journal articles | 2013

Goodrich CS, 2013, 'Positive solutions to differential inclusions with nonlocal, nonlinear boundary conditions', Applied Mathematics and Computation, 219, pp. 11071 - 11081,

Journal articles | 2012

Ferreira RAC; Goodrich CS, 2012, 'Positive solution for a discrete fractional periodic boundary value problem', Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 19, pp. 545 - 557

Journal articles | 2012

Goodrich CS, 2012, 'Nonlocal systems of BVPs with asymptotically superlinear boundary conditions', Commentationes Mathematicae Universitatis Carolinae, 53, pp. 79 - 97

Journal articles | 2012

Goodrich CS, 2012, 'Nonlocal systems of bvps with asymptotically sublinear boundary conditions', Applicable Analysis and Discrete Mathematics, 6, pp. 174 - 193,

Journal articles | 2012

Goodrich CS, 2012, 'On a discrete fractional three-point boundary value problem', Journal of Difference Equations and Applications, 18, pp. 397 - 415,

Journal articles | 2012

Goodrich CS, 2012, 'On a first-order semipositone discrete fractional boundary value problem', Archiv der Mathematik, 99, pp. 509 - 518,

Journal articles | 2012

Goodrich CS, 2012, 'On a fractional boundary value problem with fractional boundary conditions', Applied Mathematics Letters, 25, pp. 1101 - 1105,

Journal articles | 2012

Goodrich CS, 2012, 'On discrete fractional boundary value problems with nonlocal, nonlinear boundary conditions', Communications in Applied Analysis, 16, pp. 459 - 470

Journal articles | 2012

Goodrich CS, 2012, 'On discrete sequential fractional boundary value problems', Journal of Mathematical Analysis and Applications, 385, pp. 111 - 124,

Journal articles | 2012

Goodrich CS, 2012, 'On nonlocal BVPs with nonlinear boundary conditions with asymptotically sublinear or superlinear growth', Mathematische Nachrichten, 285, pp. 1404 - 1421,

Journal articles | 2012

Goodrich CS, 2012, 'Positive solutions to boundary value problems with nonlinear boundary conditions', Nonlinear Analysis, Theory, Methods and Applications, 75, pp. 417 - 432,

Journal articles | 2012

Goodrich CS, 2012, 'The existence of a positive solution to a second-order deltanabla p-Laplacian BVP on a time scale', Applied Mathematics Letters, 25, pp. 157 - 162,

Journal articles | 2011

Goodrich CS, 2011, 'Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions', Computers and Mathematics with Applications, 61, pp. 191 - 202,

Journal articles | 2011

Goodrich CS, 2011, 'Existence of a positive solution to a first-order p-Laplacian BVP on a time scale', Nonlinear Analysis, Theory, Methods and Applications, 74, pp. 1926 - 1936,

Journal articles | 2011

Goodrich CS, 2011, 'Existence of a positive solution to a system of discrete fractional boundary value problems', Applied Mathematics and Computation, 217, pp. 4740 - 4753,

Journal articles | 2011

Goodrich CS, 2011, 'Existence of a positive solution to systems of differential equations of fractional order', Computers and Mathematics with Applications, 62, pp. 1251 - 1268,

Journal articles | 2011

Goodrich CS, 2011, 'On positive solutions to nonlocal fractional and integer-order difference equations', Applicable Analysis and Discrete Mathematics, 5, pp. 122 - 132,

Journal articles | 2011

Goodrich CS, 2011, 'Some new existence results for fractional difference equations', International Journal of Dynamical Systems and Differential Equations, 3, pp. 145 - 162,

Journal articles | 2010

Goodrich CS, 2010, 'Continuity of solutions to discrete fractional initial value problems', Computers and Mathematics with Applications, 59, pp. 3489 - 3499,

Journal articles | 2010

Goodrich CS, 2010, 'Existence of a positive solution to a class of fractional differential equations', Applied Mathematics Letters, 23, pp. 1050 - 1055,

Journal articles | 2007

Goodrich CS; Matache MT, 2007, 'The stabilizing effect of noise on the dynamics of a Boolean network', Physica A: Statistical Mechanics and its Applications, 379, pp. 334 - 356,

I am interested in nonlocal differential and difference equations. I have studied such problems both in the context of nonlocal boundary value problems but also in the context of fractional calculus (both discrete and continuous), which involves inherently nonlocal operators. I also have an interest in regularity theory for elliptic PDEs and minimizers of variational problems, and I am particularly interested in problems that involve rough or discontinuous coefficients and how such coefficients affect the regularity of any solution or minimizer.

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