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