Existence and regularity results for a Neumann problem with mixed local and nonlocal diffusion

Journal of Differential Equations, Volume 423, 5 April 2025, Pages 97-117 In this paper, we consider an elliptic problem driven by a mixed local-nonlocal operator with drift and subject to nonlocal Neumann condition. We prove the existence and uniqueness of a solution $u\in W^{2,p}(\Omega)$ of the c...

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Bibliographic Details
Main Authors Cowan, Craig, Smaily, Mohammad El, Feulefack, Pierre Aime
Format Journal Article
LanguageEnglish
Published 27.06.2024
Subjects
Mathematics - Analysis of PDEs
Mathematics - Functional Analysis
Mathematics - Mathematical Physics
Physics - Mathematical Physics
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DOI10.48550/arxiv.2406.19572

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Summary:Journal of Differential Equations, Volume 423, 5 April 2025, Pages 97-117 In this paper, we consider an elliptic problem driven by a mixed local-nonlocal operator with drift and subject to nonlocal Neumann condition. We prove the existence and uniqueness of a solution $u\in W^{2,p}(\Omega)$ of the considered problem with $L^p$-source function when $p$ and $s$ are in a certain range.
DOI:10.48550/arxiv.2406.19572