Non degeneracy of critical points of the Robin function with respect to deformations of the domain

TL;DR

This paper proves that, generically, the critical points of the Robin function remain non-degenerate when the domain undergoes small deformations, ensuring stability of these points under perturbations.

Contribution

It establishes a genericity result for the non-degeneracy of Robin function critical points under domain deformations, a novel insight in potential theory.

Findings

Critical points of the Robin function are generically non-degenerate under domain deformations.

The result applies to a broad class of domain perturbations.

Provides a foundation for stability analysis of solutions in related PDE problems.

Abstract

We show a result of genericity for non degenerate critical points of the Robin function with respect to deformations of the domain