Calculus of Variations and Geometric Measure Theory

Regularity of nonlocal minimal surfaces in low dimension

Enrico Valdinoci (Università di Roma II, Tor Vergata)

created by dicastro on 09 Dec 2013

18 dec 2013 -- 17:00   [open in google calendar]

Aula Seminari - Department of Mathematics, University of Pisa


We present a full-detail proof of the fact that the only minimal cones for the nonlocal perimeter in plane are the trivial ones (equivalently, the singular set of fractional perimeter minimizers has, at most, codimension three).

As a consequence, we show that a Bernstein type result holds in this setting up to dimension three.

The technique used is quite flexible and it may be applied to obtain monotonicity and symmetry results for variational problems with quadratic energy growth. These results were obtained in collaboration with O. Savin and A. Figalli.