Positive solutions of nonlinear problems involving the square root of the Laplacian
Document typeExternal research report
Rights accessOpen Access
We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.
Is part of[prepr200908CabT]