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.

Continuity and density results for a one-phase nonlocal free boundary problem / S. Dipierro, E. Valdinoci. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 34:6(2017), pp. 1387-1428.

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

S. Dipierro;E. Valdinoci
2017

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.
fractional harmonic replacement; fractional operators; free boundary problems; nonlocal minimal surfaces; regularity theory; analysis; mathematical physics
Settore MAT/05 - Analisi Matematica
   Elliptic Pdes and Symmetry of Interrfaces and Layers for Odd Nonlinearties
   EPSILON
   EUROPEAN COMMISSION
   FP7
   277749
2017
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/549540
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