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arXiv · 2406.19572

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

Craig Cowan·Mohammad El Smaily·Pierre Aime Feulefack
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Abstract

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.

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Craig Cowan, Mohammad El Smaily, Pierre Aime Feulefack. 2024-06-27. Existence and regularity results for a Neumann problem with mixed local and nonlocal diffusion. https://doi.org/10.1016/j.jde.2024.12.029

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