JournalsaihpcVol. 34, No. 6pp. 1387–1428

Continuity and density results for a one-phase nonlocal free boundary problem

  • Serena Dipierro

    School of Mathematics and Statistics, University of Melbourne, 813 Swanston Street, Parkville, VIC 3010, Australia
    ORCID

  • Enrico Valdinoci

    School of Mathematics and Statistics, University of Melbourne, 813 Swanston Street, Parkville, VIC 3010, Australia; Weierstraß Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany; Dipartimento di Matematica Federigo Enriques, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy; Istituto di Matematica Applicata e Tecnologie Informatiche Enrico Magenes, Consiglio Nazionale delle Ricerche, Via Ferrata 1, 27100 Pavia, Italy
    ORCID
Continuity and density results for a one-phase nonlocal free boundary problem cover
Download PDF

Abstract

We consider a one-phase nonlocal free boundary problem obtained by the superposition of a fractional Dirichlet energy plus a nonlocal perimeter functional. We prove that the minimizers are Hölder continuous and the free boundary has positive density from both sides.

For this, we also introduce a new notion of fractional harmonic replacement in the extended variables and we study its basic properties.

Cite this article

Serena Dipierro, Enrico Valdinoci, Continuity and density results for a one-phase nonlocal free boundary problem. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 6, pp. 1387–1428

DOI 10.1016/J.ANIHPC.2016.11.001