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Continuity and differentiability for weighted Sobolev spaces |
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| Authors: | Yoshihiro Mizuta Tetsu Shimomura |
| Affiliation: | The Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima 739-8521, Japan Tetsu Shimomura ; Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan |
| Abstract: | Our aim in this paper is to discuss continuity and differentiability of functions in weighted Sobolev spaces in the limiting case of Sobolev's imbedding theorem. |
| Keywords: | H" {o}lder continuity, differentiability, weighted Sobolev spaces, $A_p$-weight, $p$-Poincar'{e} inequality, Sobolev's imbedding theorem |
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