Optimal boundary regularity for mixed local and nonlocal equations

2025/07/18 by Nicola Abatangelo, Abatangelo, Nicola, Elisa Affili +3
Mathematics · #Nonlinear Partial Differential Equations #Differential Equations and Boundary Problems #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2507.13711

Abstract

We provide sharp boundary regularity estimates for solutions to elliptic equations driven by an integro-differential operator obtained as the sum of a Laplacian with a nonlocal operator generalizing a fractional Laplacian. Our approach makes use of weighted Hölder spaces as well as regularity estimates for the Laplacian in this context and a fixed-point argument. We show the optimality of the obtained estimates by means of a counterexample that we have striven to keep as explicit as possible.

Citations

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Related

• On some regularity properties of mixed local and nonlocal elliptic equations
• Regularity theory for mixed local-nonlocal problem involving general stable operators
• Optimal regularity for nonlocal elliptic equations and free boundary problems
• Boundary regularity for nonlocal elliptic equations over Reifenberg flat domains
• Mixed local and nonlocal elliptic operators: regularity and maximum\n principles