Journal
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Volume 30, Issue 1-3, Pages 59-65Publisher
TAYLOR & FRANCIS INC
DOI: 10.1081/PDE-200044445
Keywords
Hardy-Littlewood-Sobolev inequalities; systems of integral equations; radial symmetry; monotonicity; moving planes in integral forms
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Under the natural integrability conditions u is an element of LP+1 (R-n) and v is an element of Lq+1 (R-n), we prove that all the solutions are radially symmetric and monotonic decreasing about some point. To prove this result, we introduce an integral form of the method of moving planes that is quite different front the traditional method of moving planes for PDES. We expect to see applications of this new method to many problems.
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