Different degrees of non-compactness for optimal Sobolev embeddings |
| |
| Affiliation: | 1. Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210-1174, United States of America;2. Charles University, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Sokolovská 83, 186 75 Praha 8, Czech Republic;3. Czech Technical University in Prague, Faculty of Electrical Engineering, Department of Mathematics, Technická 2, 166 27 Praha 6, Czech Republic |
| |
| Abstract: | The structure of non-compactness of optimal Sobolev embeddings of m-th order into the class of Lebesgue spaces and into that of all rearrangement-invariant function spaces is quantitatively studied. Sharp two-sided estimates of Bernstein numbers of such embeddings are obtained. It is shown that, whereas the optimal Sobolev embedding within the class of Lebesgue spaces is finitely strictly singular, the optimal Sobolev embedding in the class of all rearrangement-invariant function spaces is not even strictly singular. |
| |
| Keywords: | Sobolev spaces Compactness Bernstein numbers Singular operators |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
