On the Robin function for the Fractional Laplacian on symmetric domains

TL;DR

This paper proves the non-degeneracy of critical points of the Robin function for the fractional Laplacian in symmetric, convex domains, extending classical results to fractional operators.

Contribution

It extends classical Laplacian results to the fractional setting, establishing non-degeneracy of Robin function critical points under symmetry and convexity.

Findings

Critical points of the Robin function are non-degenerate in symmetric convex domains.

The results generalize Grossi's classical Laplacian findings to fractional Laplacians.

The work provides new insights into the structure of fractional elliptic operators.

Abstract

In this work we prove the non-degeneracy of the critical points of the Robin function for the Fractional Laplacian under symmetry and convexity assumptions on the domain $\Omega$. This work extends to the fractional setting the results of M. Grossi concerning the classical Laplace operator.