WIAS Preprint No. 2281, (2016)

Nonlocal minimal surfaces: Interior regularity, quantitative estimates and boundary stickiness



Authors

  • Dipierro, Serena
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 49Q05 53A10 58E12 35R11

Keywords

  • nonlocal minimal surfaces, regularity theory and applications

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, referring to the papers [CRS10, SV13, CV13, BFV14, FV, DSV15, CSV16] for full details.

Appeared in

  • Recent Developments in Nonlocal Theory, G. Palatucci, T. Kuusi, eds., Sciendo, de Gruyter, 2018, pp. 165--209.

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