On the critical points of semi-stable solutions on convex domains of Riemannian surfaces

Massimo Grossi; Luigi Provenzano

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arXiv · 2306.10641

On the critical points of semi-stable solutions on convex domains of Riemannian surfaces

Massimo Grossi·Luigi Provenzano

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Abstract

In this paper we consider semilinear equations $-Δu=f(u)$ with Dirichlet boundary conditions on certain convex domains of the two dimensional model spaces of constant curvature. We prove that a positive, semi-stable solution $u$ has exactly one non-degenerate critical point (a maximum). The proof consists in relating the critical points of the solution with the critical points of a suitable auxiliary function, jointly with a topological degree argument.

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BibTeX RIS

Massimo Grossi, Luigi Provenzano. 2023-06-27. On the critical points of semi-stable solutions on convex domains of Riemannian surfaces. https://arxiv.org/abs/2306.10641

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