Entropy solutions of Dirichlet problem for a class of nonlinear elliptic high-order equations with L¹-data
In this paper we study Dirichlet problem for nonlinear elliptic high-order equations with coefficients satisfying a strengthened ellipticity condition. A class of nonlinear high-order equations with such a condition on coefficients and data which are within usual theory of monotone operators [7] has...
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| Veröffentlicht in: | Нелинейные граничные задачи |
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| Datum: | 2002 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2002
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/169222 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Entropy solutions of Dirichlet problem for a class of nonlinear elliptic high-order equations with L¹-data / A.A. Kovalevsky // Нелинейные граничные задачи. — 2002. — Т. 12. — С. 119-127. — Бібліогр.: 9 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | In this paper we study Dirichlet problem for nonlinear elliptic high-order equations with coefficients satisfying a strengthened ellipticity condition. A class of nonlinear high-order equations with such a condition on coefficients and data which are within usual theory of monotone operators [7] has been introduced in [9], where Holder continuity of generalized solutions of equations of that class has been established. Unlike [9] equations under consideration in the present paper have L¹-right-hand sides. Their solvability does not follow directly from results of the theory of monotone operators and on the whole it is a rather difficult problem.
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| ISSN: | 0236-0497 |