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, referring to the papers [8, 27, 10, 3, 20, 19, 12] for full details.
|Title of host publication||Recent Developments in Nonlocal Theory|
|Editors||G Palatucci, T Kuusi|
|Place of Publication||Poland|
|Publisher||Walter de Gruyter|
|Number of pages||45|
|Publication status||Published - 2018|