Stable nonlocal minimal surfaces and phase transitions

par Joaquim Serra (Universitat Polytècnica de Catalunya)

mardi 31 mai 2016, 14:00 → 15:00 Europe/Paris

Fokko Du Cloux (Université Claude Bernard Lyon 1 - Campus de la Doua, Bâtiment Braconnier)

We will introduce the results of a recent joint work with Cinti and Valdinoci, in which we study stable and minimizing nonlocal minimal surfaces. First, we will explain some new quantitative flatness and BV type estimates for stable and minimizing nonlocal minimal surfaces. We will also explain the key ingredients in the proofs of these estimates, which do not have a counterpart in the theory of classical minimal surfaces. Second, we will discuss the same type of estimates for stable solutions to nonlocal Allen Cahn equations, and the implications they have in classification of entire solutions ---which we study in a forthcoming paper with Cabré and Cinti.