Regularity results for nonlocal minimal graphs
A talk in the Oberseminar Analysis series by
Matteo Cozzi
| Abstract: | Nonlocal minimal surfaces are hypersurfaces of Euclidean space that minimize the fractional perimeter, a geometric functional introduced in 2010 by Caffarelli, Roquejoffre & Savin in connection with phase transition problems displaying long-range interactions.
In this talk, I will introduce these objects, describe the most important progresses made so far in their analysis, and discuss the most challenging open questions.
I will then focus on the particular case of nonlocal minimal graphs and present some recent results on their regularity obtained in collaboration with X. Cabré (ICREA & UPC Barcelona). If time permits, I will also discuss some rigidity results recently obtained with A. Farina (Université de Picardie) and L. Lombardini (Università di Milano). |