Gamma convergence of an energy functional related to the fractional Laplacian

TL;DR

This paper establishes a Gamma-convergence result for an energy functional involving fractional Laplacian operators with singular perturbations inside the domain and on its boundary, advancing the mathematical understanding of such nonlocal operators.

Contribution

It introduces a novel Gamma-convergence analysis for energy functionals with fractional Laplacians and dual singular perturbations, extending previous local operator results.

Findings

Gamma-convergence proven for the energy functional

Handles singular perturbations both in interior and boundary

Advances mathematical understanding of fractional Laplacian energies

Abstract

We prove a Gamma-convergence result for an energy functional related to some fractional powers of the Laplacian operator, with two singular perturbations (one in the interior and one on the boundary).