A nonlocal free boundary problem

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Date
2014
Volume
2042
Issue
Journal
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract

We consider a nonlocal free boundary problem built by a fractional Dirichlet norm plus a fractional perimeter. Among other results, we prove a monotonicity formula for the minimizers, glueing lemmata, uniform energy bounds, convergence results, a regularity theory for the planar cones and a trivialization result for the flat case. Several classical free boundary problems are limit cases of the one that we consider in this paper.

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Keywords
Fractional perimeter, minimization problem, monotonicity formula, classification of cones
Citation
Dipierro, S., Savin, O., & Valdinoci, E. (2014). A nonlocal free boundary problem (Vol. 2042). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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