Positive solutions of nonlinear problems involving the square root of the Laplacian

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229772We 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.Analysis of PDEsPositive solutions of nonlinear problems involving the square root of the Laplaciantext