Symmetry of positive solutions of fractional Laplacian equation and system with Hardy–Sobolev exponent on the unit ball

In this work, we consider a class of Hardy–Sobolev differential equations and systems involving the fractional Laplacian on the unit ball. We first show the differential equations and systems are equivalent to some integral equations and systems, respectively. Then applying the method of moving plan...

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Bibliographic Details
Published in:Journal of pseudo-differential operators and applications 2015-12, Vol.6 (4), p.503-519
Main Authors: Zhao, Junping, Dou, Jingbo, Zhou, Huaiyu
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Functional Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Partial Differential Equations
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Summary:In this work, we consider a class of Hardy–Sobolev differential equations and systems involving the fractional Laplacian on the unit ball. We first show the differential equations and systems are equivalent to some integral equations and systems, respectively. Then applying the method of moving planes in the integral forms, we prove the radial symmetry of positive solutions.
ISSN:1662-9981
1662-999X
DOI:10.1007/s11868-015-0131-y