Non-degeneracy and uniqueness of solutions to singular mean field equations on bounded domains

Abstract

The aim of this paper is to complete the program initiated in [50], [23] and then carried out by several authors concerning non-degeneracy and uniqueness of solutions to mean field equations. In particular, we consider mean field equations with general singular data on non-smooth domains. The argument is based on the Alexandrov-Bol inequality and on the eigenvalues analysis of linearized singular Liouville-type problems.

References in corpus (10)

• The sphere covering inequality and its dual
• An improved geometric inequality via vanishing moments, with applications to singular Liouville equations
• Non degeneracy, Mean Field Equations and the Onsager theory of 2D turbulence
• Supercritical Mean Field Equations on convex domains and the Onsager's statistical description of two-dimensional turbulence
• On multiplicity bounds for Schrodinger eigenvalues on Riemannian surfaces
• Self gravitating cosmic strings and the Alexandrov's inequality for Liouville-type equations
• On a singular Liouville-type equation and the Alexandrov isoperimetric inequality
• Uniqueness of solutions of mean field equations in ${\mathbb{R}}^2$
• Uniqueness of bubbling solutions of mean field equations
• Global bifurcation analysis of mean field equations and the Onsager microcanonical description of two-dimensional turbulence

Cited by in corpus (6)

• A singular Sphere Covering Inequality: uniqueness and symmetry of solutions to singular Liouville-type equations
• Local uniqueness and non-degeneracy of blow up solutions of mean field equations with singular data
• On $SU(3)$ Toda system with multiple singular sources
• Non-degeneracy and uniqueness of solutions to general singular Toda systems on bounded domains
• Existence results for a non-relativistic Chern-Simons model with purely mutual interaction
• On the first eigenvalue of Liouville-type problems