О G-сходимости нелинейных эллиптических операторов, связанных с задачей Дирихле в переменных областях
A notion of G-convergence of operators As:Ws→W∗s to the operator A:W→W∗ is introduced and studied under certain connection conditions for the Banach spaces Ws,s=1,2,..., and the Banach space W. It has been established that the connection conditions for abstract space are satisfied by the Sobolev spa...
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| Datum: | 1993 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Russian |
| Veröffentlicht: |
Інститут математики НАН України
1993
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| Schriftenreihe: | Український математичний журнал |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | О G-сходимости нелинейных эллиптических операторов, связанных с задачей Дирихле в переменных областях / А.А. Ковалевский // Український математичний журнал. — 1993. — Т. 45, № 7. — С. 948–962. — Бібліогр.: 13 назв. — рос. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | A notion of G-convergence of operators As:Ws→W∗s to the operator A:W→W∗ is introduced and studied under certain connection conditions for the Banach spaces Ws,s=1,2,..., and the Banach space W. It has been established that the connection conditions for abstract space are satisfied by the Sobolev spaces W∘k,m(Ωs),W∘k,m(Ω) ({Ωs} is a sequence of perforated domains contained in a bounded domain Ω⊂ℝn). Hence, the results obtained for abstract operators can be applied to the operators of Dirichlet problems in the domains Ωs. |
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