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

Craig Cowan; Mohammad El Smaily; Pierre Aime Feulefack

doi:10.1016/j.jde.2024.12.029

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

Analysis of PDEs 2025-01-03 v1 Mathematical Physics Functional Analysis math.MP

Authors: 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.

Keywords

regularity for elliptic equations nonlocal equations elliptic partial differential equations

Cite

@article{arxiv.2406.19572,
  title  = {Existence and regularity results for a Neumann problem with mixed local and nonlocal diffusion},
  author = {Craig Cowan and Mohammad El Smaily and Pierre Aime Feulefack},
  journal= {arXiv preprint arXiv:2406.19572},
  year   = {2025}
}

Comments

18 pages

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