# A variant of the Alt-Caff arelli-Friedman problem for the localization of eigenfunctions

## Guy David

### (Université de Paris-Sud)

Date: Oct 08, 2013, time: 10:40

Abstract. This may be subject to change.
The localization problem concerns eigenfunctions for an elliptic operator (for instance, Laplacian on a complicated domain, or Schrodinger on a simple one).
We (with M. Filoche, D. Jerison, S. Mayboroda) propose
a free boundary problem to find subregions where the eigenfunctions are likely to be localized, and study regularity properties of the minimizers.