2015/04/21 by Serena Dipierro, Enrico Valdinoci, Dipierro, Serena +1
Mathematics · #Differential Equations and Boundary Problems #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1504.05569
We consider a one-phase nonlocal free boundary problem obtained by the\nsuperposition of a fractional Dirichlet energy plus a nonlocal perimeter\nfunctional. We prove that the minimizers are H "older continuous and the free\nboundary has positive density from both sides.\n For this, we also introduce a new notion of fractional harmonic replacement\nin the extended variables and we study its basic properties.\n