Publication Date:
2017
Citation:
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.
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.
For this, we also introduce a new notion of fractional harmonic replacement in the extended variables and we study its basic properties.
IRIS type:
01 - Articolo su periodico
Keywords:
fractional harmonic replacement; fractional operators; free boundary problems; nonlocal minimal surfaces; regularity theory; analysis; mathematical physics
List of contributors:
S. Dipierro, E. Valdinoci
Link to information sheet: