Estimates for capacities and traces of potentials
It is shown that isoperimetric inequalities, relating measures and capacities, hold for all sets in ℝn if they are valid for all balls. As a corollary, the necessary and sufficient conditions for the continuity of some imbeddings of M. Riesz and Bessel potential spaces are obtained. The introduction...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171284000053 |
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| author | V. G. Maz'ja S. P. Preobrazenskii |
| author_facet | V. G. Maz'ja S. P. Preobrazenskii |
| author_sort | V. G. Maz'ja |
| collection | DOAJ |
| description | It is shown that isoperimetric inequalities, relating measures and capacities, hold for all sets in ℝn if they are valid for all balls. As a corollary, the necessary and sufficient conditions for the continuity of some imbeddings of M. Riesz and Bessel potential spaces are obtained. The introduction contains a survey of known results on inequalities of Sobolev type. |
| format | Article |
| id | doaj-art-bfc57b3ac277473c9c90389b602f4f99 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-bfc57b3ac277473c9c90389b602f4f992025-02-03T07:24:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-0171416310.1155/S0161171284000053Estimates for capacities and traces of potentialsV. G. Maz'ja0S. P. Preobrazenskii1Institute of Mathematics and Mechanics, Leningrad University, Leningrad, RussiaDepartment of Mathematics, Leningrad Polytechnical Institute, Leningrad, RussiaIt is shown that isoperimetric inequalities, relating measures and capacities, hold for all sets in ℝn if they are valid for all balls. As a corollary, the necessary and sufficient conditions for the continuity of some imbeddings of M. Riesz and Bessel potential spaces are obtained. The introduction contains a survey of known results on inequalities of Sobolev type.http://dx.doi.org/10.1155/S0161171284000053Sobolev spacesBessel potential spacesimbedding theoremscapacitiesisoperimetric inequalities. |
| spellingShingle | V. G. Maz'ja S. P. Preobrazenskii Estimates for capacities and traces of potentials International Journal of Mathematics and Mathematical Sciences Sobolev spaces Bessel potential spaces imbedding theorems capacities isoperimetric inequalities. |
| title | Estimates for capacities and traces of potentials |
| title_full | Estimates for capacities and traces of potentials |
| title_fullStr | Estimates for capacities and traces of potentials |
| title_full_unstemmed | Estimates for capacities and traces of potentials |
| title_short | Estimates for capacities and traces of potentials |
| title_sort | estimates for capacities and traces of potentials |
| topic | Sobolev spaces Bessel potential spaces imbedding theorems capacities isoperimetric inequalities. |
| url | http://dx.doi.org/10.1155/S0161171284000053 |
| work_keys_str_mv | AT vgmazja estimatesforcapacitiesandtracesofpotentials AT sppreobrazenskii estimatesforcapacitiesandtracesofpotentials |