Nonlocal minimal surfaces: Interior regularity, quantitative estimates and boundary stickiness
- Dipierro, Serena
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 49Q05 53A10 58E12 35R11
- nonlocal minimal surfaces, regularity theory and applications
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 [CRS10, SV13, CV13, BFV14, FV, DSV15, CSV16] for full details.
- Recent Developments in Nonlocal Theory, G. Palatucci, T. Kuusi, eds., Sciendo, de Gruyter, 2018, pp. 165--209.