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This article is cited in 9 scientific papers (total in 9 papers)
Solvability of the Dirichlet problem for second-order elliptic equations
V. Zh. Dumanyan Yerevan State University, Yerevan, Armenia
Abstract:
In our preceding papers, we obtained necessary and sufficient conditions for the existence of an $(n{-}1)$-dimensionally continuous solution of the Dirichlet problem in a bounded domain $Q\subset\mathbb R_n$ under natural restrictions imposed on the coefficients of the general second-order elliptic equation, but these conditions were formulated in terms of an auxiliary operator equation in a special Hilbert space and are difficult to verify. We here obtain necessary and sufficient conditions for the problem solvability in terms of the initial problem for a somewhat narrower class of right-hand sides of the equation and also prove that the obtained conditions become the solvability conditions in the space $W_2^1(Q)$ under the additional requirement that the boundary function belongs to the space $W_2^{1/2}(\partial Q)$.
Keywords:
Dirichlet problem, elliptic equation.
Received: 28.02.2014 Revised: 27.03.2014
Citation:
V. Zh. Dumanyan, “Solvability of the Dirichlet problem for second-order elliptic equations”, TMF, 180:2 (2014), 189–205; Theoret. and Math. Phys., 180:2 (2014), 917–931
Linking options:
https://www.mathnet.ru/eng/tmf8670https://doi.org/10.4213/tmf8670 https://www.mathnet.ru/eng/tmf/v180/i2/p189
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Abstract page: | 483 | Full-text PDF : | 175 | References: | 80 | First page: | 53 |
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