Salvador Villegas

activity

20242026

collaborators

5 papers

math.AP2026

Lack of interior $L^{q}$ bounds for stable solutions to elliptic equations

Salvador Villegas

We consider stable solutions of semilinear elliptic equations of the form $- Δ u = f (u)$ in a bounded domain $Ω \subset R^{N}$ . In a well-known paper \cite{cfrs}, Cabré, Figalli,…

math.AP2026

Regularity of stable radial solutions to semilinear elliptic equations in MEMS problems

Fa Peng, Salvador Villegas

This paper investigates the regularity of stable radial solutions to semilinear elliptic equations arising in MEMS problems, modeled by the Dirichlet problem $- Δ u = f (u)$ in the unit…

math.AP2025

A priori estimates of stable solutions of the general Hardy-Henon equation in the ball

J. Silverio Martinez-Baena, Salvador Villegas

This paper is devoted to the study of semi-stable radial solutions $u \in H^{1} (B_{1})$ of $-Δu=\vert x\vert^αf(u) \mbox{ in } B_1\setminus\lbrace0\rbrace$, where $f \in C^{1} (R)$ …

math.AP2025

Solutions for autonomous semilinear elliptic equations

Alexis Molino, Salvador Villegas

We study existence of nontrivial solutions to problem \begin{equation*} \left\lbrace \begin{array}{rcll} -Δu &=& λu+f(u)&\text{ in }Ω,\\ u&=&0&\text{ on }\partial Ω, \end{array}\ri…

math.AP2024

A negative result on regularity estimates on finite radial Morse index solutions to elliptic problems