Serena Dipierro and Enrico Valdinoci
Nonlocal minimal surfaces: interior regularity, quantitative estimates and boundary stickiness
(870K, pdf)

ABSTRACT.  We consider surfaces which minimize a nonlocal perimeter functional and we discuss their interior regularity and rigidity properties, in a quantitative and qualitative way, and their (perhaps rather surprising) boundary behavior. We present at least a sketch of the proofs of these results, in a way that aims to be as elementary and self contained as possible.