(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Dipierro, Serena; Valdinoci, Enrico
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.
