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

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

2009-05-08

arxiv.org/abs/0905.1257v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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