A nonlocal free boundary problem

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Date
2014
Volume
2042
Issue
Journal
Series Titel
WIAS Preprints
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Link to publishers version
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
Dipierro, S., Savin, O., & Valdinoci, E. (2014). A nonlocal free boundary problem (Vol. 2042). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
License
This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.