Qualitative analysis on the critical points of the Robin function

  • Francesca Gladiali

    Università degli Studi di Sassari, Sassari, Italy
  • Massimo Grossi

    Sapienza Università di Roma, Roma, Italy
  • Peng Luo

    Central China Normal University, Wuhan, P. R. China
  • Shusen Yan

    Central China Normal University, Wuhan, P. R. China
Qualitative analysis on the critical points of the Robin function cover
Download PDF

A subscription is required to access this article.

Abstract

Let be a smooth bounded domain with and , where is the ball centered at with radius . In this paper, we establish the number, location and non-degeneracy of critical points of the Robin function in for small enough. We will show that the location of plays a crucial role in the existence and multiplicity of the critical points. The proof of our result is a consequence of delicate estimates on the Green’s function near . Some applications to computing the exact number of solutions of related well-studied nonlinear elliptic problems are shown.

Cite this article

Francesca Gladiali, Massimo Grossi, Peng Luo, Shusen Yan, Qualitative analysis on the critical points of the Robin function. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1459