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arXiv · 2507.13711

Optimal boundary regularity for mixed local and nonlocal equations

Nicola Abatangelo·Elisa Affili·Matteo Cozzi
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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 H\"older 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.

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Nicola Abatangelo, Elisa Affili, Matteo Cozzi. 2025-07-18. Optimal boundary regularity for mixed local and nonlocal equations. https://arxiv.org/abs/2507.13711

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