Continuity and density results for a one-phase nonlocal free boundary problem
- Dipierro, Serena
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 35R35 49N60 35R11, 35A15
- Free boundary problems, nonlocal minimalsurfaces, fractional operators, regularity theory, fractional harmonic replacement
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 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.
- Ann. Inst. H. Poincare Anal. Non Lineaire, 34 (2017), pp. 1387-1428.