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

Xavier Cabre; Jinggang Tan

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arXiv · 0905.1257

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

Xavier Cabre·Jinggang Tan

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Abstract

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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Xavier Cabre, Jinggang Tan. 2009-05-08. Positive solutions of nonlinear problems involving the square root of the Laplacian. https://arxiv.org/abs/0905.1257

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