An optimal mass transport approach for limits of eigenvalue problems for the fractional $p$-Laplacian

TL;DR

This paper uses optimal mass transport theory to interpret the limits of eigenvalue problems for fractional p-Laplacian operators as p approaches infinity, considering both Dirichlet and Neumann boundary conditions.

Contribution

It introduces a novel interpretation of eigenvalue limits for fractional p-Laplacian operators using optimal mass transport theory, covering different boundary conditions.

Findings

Eigenvalue problems for fractional p-Laplacian are interpreted via optimal mass transport.

The approach applies to both Dirichlet and Neumann boundary conditions.

Provides a new perspective on the asymptotic behavior of eigenvalues as p approaches infinity.

Abstract

We find interpretation using optimal mass transport theory for eigenvalue problems obtained as limits of the eigenvalue problems for the fractional $p-$Laplacian operators as $p\to +\infty$. We deal both with Dirichlet and Neumann boundary conditions.