10 may 2016 -- 14:30
Aula Dal Passo, Dip.Matematica, Università "Tor Vergata", Roma
Abstract.
We give an introductory exposition about some surfaces which minimize a nonlocal perimeter functional. These objects naturally arise in the study of the interfaces of phase transitions, when the particles exhibit long-range interactions or when boundary effects are present. In addition, these nonlocal minimal surfaces have concrete applications in several areas, such as image processing and mathematical biology. We will present some results concerning interior regularity and rigidity of nonlocal minimal surfaces, with some quantitative estimates and some qualitative descriptions in several examples. We will describe also the (rather unusual) boundary behavior of these object and their connection with the fractional Allen-Cahn equation.