Fractional Eigenvalues

TL;DR

This paper investigates the behavior of eigenvalues and solutions for a non-local fractional eigenvalue problem as the parameter p approaches infinity, revealing unique properties and complex eigenvalue behavior.

Contribution

It introduces the limit equation for large p in fractional Sobolev spaces and analyzes the properties of viscosity solutions and eigenvalues in this regime.

Findings

Eigenvalues exhibit unusual behavior as p increases.

Viscosity solutions have notable properties.

Derived the limit equation for large p.

Abstract

We study a non-local eigenvalue problem related to the fractional Sobolev spaces for large values of p and derive the limit equation as p goes to infinity. Its viscosity solutions have many interesting properties and the eigenvalues exhibit a strange behaviour. Keywords: eigenvalue, non-local equation, non-linear equation