Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 263, Issue 8, Pages 2205-2227Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2012.06.018
Keywords
Fractional Laplacian; Nonexistence; Star-shaped domain; Caffarelli-Silvestre extension
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Funding
- Alexander von Humboldt foundation
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In this paper we study a class of fractional elliptic problems of the form { (-Delta)(s)u = f(x, u) in Omega, u = 0 in R-N\Omega, where s is an element of (0, 1). We prove nonexistence of positive solutions when Omega is star-shaped and is supercritical. We also derive a nonexistence result for subcritical f in some unbounded domains. The argument relics on the method of moving spheres applied to a reformulated problem using the Caffarelli-Silvestre extension (Caffarelli and Silvestre (2007) [11]) of a solution of the above problem. (C) 2012 Elsevier Inc. All rights reserved.
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