Eigenvalues homogenization for the fractional $p-$Laplacian operator

TL;DR

This paper investigates how eigenvalues of the fractional p-Laplacian operator behave under homogenization in bounded domains, providing convergence results and explicit rates for both Dirichlet and Neumann boundary conditions.

Contribution

It offers the first detailed analysis of eigenvalue homogenization for the fractional p-Laplacian, including convergence proofs and explicit convergence rates.

Findings

Eigenvalues converge under homogenization.

Explicit order of convergence rates established.

Results apply to both Dirichlet and Neumann conditions.

Abstract

In this work we study the homogenization for eigenvalues of the fractional $p-$Laplace in a bounded domain both with Dirichlet and Neumann conditions. We obtain the convergence of eigenvalues and the explicit order of the convergence rates.