Optimal boundary regularity for mixed local and nonlocal equations

Mathematics in Engineering 2026 Open access

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Authors: Nicola Abatangelo, Elisa Affili, Matteo Cozzi, Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS-Université de Rouen Normandie, Avenue de l'Université BP.12, 76801 Saint-Étienne-du-Rouvray, France
DOI: 10.3934/mine.2026001
Cited by: 0
References: 15

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.

Fields of Study & Subjects

Nonlinear Partial Differential Equations Differential Equations and Boundary Problems Fractional Differential Equations Solutions

Publication details

Journal / source
Mathematics in Engineering
Volume
8
Issue
1
Pages
1–42
Publication date
1 January 2026
Language
EN