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

By Serena Dipierro, Enrico Valdinoci. 2016

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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.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/b4f79ea6095b0f25676c88a114405251f3253760