Compact Sobolev embedding theorems involving symmetry and its application |
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Authors: | Juanjuan Gao Peihao Zhao Yong Zhang |
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Affiliation: | (1) Kansas State University, Manhattan, KS, U.S.A;(2) Carnegie Mellon University, Pittsburgh, PA, U.S.A |
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Abstract: | Given a bounded regular domain with cylindrical symmetry, functions having such symmetry and belonging to W 1,p can be embedded compactly into some weighted L q spaces, with q superior to the critical Sobolev exponent. A similar result is also obtained for variable exponent Sobolev space W 1,p(x). Furthermore, we give a simple application to the p(x)-Laplacian problem. |
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