A local and nonlocal coupling model involving the $p$-Laplacian

Uriel Kaufmann; Raúl Vidal

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arXiv · 2508.20951

A local and nonlocal coupling model involving the $p$-Laplacian

Uriel Kaufmann·Raúl Vidal

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Abstract

In this paper we extend some results presented in \cite{julio} to the case of the $p$-Laplacian operator. More precisely, we consider a model that couples a local $p$-Laplacian operator with a nonlocal $p$-Laplacian operator through source terms in the equation. The resulting problem is associated with an energy functional. We establish the existence and uniqueness of a solution, which is obtained via the direct minimization of the corresponding energy functional.

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Uriel Kaufmann, Raúl Vidal. 2025-08-28. A local and nonlocal coupling model involving the $p$-Laplacian. https://arxiv.org/abs/2508.20951

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