Journal
ADVANCES IN MATHEMATICS
Volume 224, Issue 5, Pages 2052-2093Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2010.01.025
Keywords
Fractional Laplacian; Critical exponent; Nonlinear mixed boundary problem; A priori estimates; Nonlinear Liouville theorems; Moving planes method
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Funding
- Spain Government [MTM2005-07660-C02-01, MTM2008-06349-C03-01]
- Catalan Government [SGR2009-345]
- CONICYT Becas de Postgrado of Chile
- Programa de Recerca del Centre de Recerca Matematica, Barcelona, Spain
- ICREA Funding Source: Custom
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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. (C) 2010 Elsevier Inc. All rights reserved.
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