Regularity of stable solutions to elliptic equations
- Iñigo Urtiaga Erneta (Universitat Politècnica de Catalunya)
Abstract
In this talk, we address the regularity problem for stable solutions to elliptic equations. Here, a solution is "stable" if the the principal eigenvalue of the linearized equation is nonnegative. In particular, for variational problems, stability amounts to the nonnegativity of the second variation and hence it includes the class of minimizers. The smoothness of stable solutions turns out to be a delicate question which depends on the dimension of the space. For instance, given a bounded domain