A local and nonlocal coupling model involving the $p$-Laplacian
Analysis of PDEs
2026-01-14 v2
Abstract
In this paper we extend some results presented in \cite{julio} to the case of the -Laplacian operator. More precisely, we consider a model that couples a local -Laplacian operator with a nonlocal -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.
Cite
@article{arxiv.2508.20951,
title = {A local and nonlocal coupling model involving the $p$-Laplacian},
author = {Uriel Kaufmann and Raúl Vidal},
journal= {arXiv preprint arXiv:2508.20951},
year = {2026}
}