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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2006, Volume 6, Issue 4, Pages 43–49
(Mi vngu244)
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Generalized Dirichlet problem for elliptic equation degenerating on unbounded manifolds
S. A. Iskhokova, G. I. Tarasovab a Institute of Mathematics, Academy of Sciences of Republic of Tajikistan, Dushanbe
b Yakutsk State University
Abstract:
In the paper we investigate the unique solvability of a generalized Dirichlet problem
for higher order elliptic equation, degenerating on unbounded $C^0$ — manifolds of arbitrary
dimension less then dimension of the space. Differential properties of the solution are studied
depending on the smoothness of coefficients of the differential operator, the right-hand side
of differential equation and boundary functions.
The method applied in the paper is based on elements of the embedding theory weighted
function spaces. Therefore in the paper first necessary imbedding theorems for the corresponding function spaces are established.
Received: 27.12.2005
Citation:
S. A. Iskhokov, G. I. Tarasova, “Generalized Dirichlet problem for elliptic equation degenerating on unbounded manifolds”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 6:4 (2006), 43–49
Linking options:
https://www.mathnet.ru/eng/vngu244 https://www.mathnet.ru/eng/vngu/v6/i4/p43
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Abstract page: | 133 | Full-text PDF : | 47 | References: | 34 | First page: | 1 |
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