Nonlocal Minimal Surfaces: Interior Regularity, Quantitative Estimates and Boundary Stickiness
Serena Dipierro, Enrico Valdinoci · 2017
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.