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

## TL;DR

This paper extends previous work to a model coupling local and nonlocal p-Laplacian operators, establishing existence and uniqueness of solutions through energy minimization.

## Contribution

It introduces a new coupled local and nonlocal p-Laplacian model and proves the existence and uniqueness of solutions using energy functional methods.

## Key findings

- Existence of solutions established
- Uniqueness of solutions proven
- Solution obtained via energy minimization

## 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.