Solvability of the Dirichlet problem for a general second-order elliptic equation
- Yerevan State University, Yerevan (Armenia)
The paper is concerned with studying the solvability of the Dirichlet problem for the second-order elliptic equation ; in a bounded domain Q subset of R{sub n}, n{>=}2, with C{sup 1}-smooth boundary and boundary condition u{sub 0} element of L{sub 2}({partial deriv}Q). Conditions for the existence of an (n-1)-dimensionally continuous solution are obtained, the resulting solvability condition is shown to be similar in form to the solvability condition in the conventional generalized setting (in W{sub 2}{sup 1}(Q)). In particular, the problem is shown to have an (n-1)-dimensionally continuous solution for all u{sub 0} element of L{sub 2}({partial deriv}Q) and all f and F from the appropriate function spaces, provided that the homogeneous problem (with zero boundary conditions and zero right-hand side) has no nonzero solutions in W{sub 2}{sup 1}(Q). Bibliography: 14 titles.
- OSTI ID:
- 21592532
- Journal Information:
- Sbornik. Mathematics, Vol. 202, Issue 7; Other Information: DOI: 10.1070/SM2011v202n07ABEH004174; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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