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Title: Solvability of the Dirichlet problem for a general second-order elliptic equation

Abstract

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.

Authors:
 [1]
  1. Yerevan State University, Yerevan (Armenia)
Publication Date:
OSTI Identifier:
21592532
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 202; Journal Issue: 7; Other Information: DOI: 10.1070/SM2011v202n07ABEH004174; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; BOUNDARY CONDITIONS; DIRICHLET PROBLEM; EQUATIONS; FUNCTIONS; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; ONE-DIMENSIONAL CALCULATIONS; SMOOTH MANIFOLDS; BOUNDARY-VALUE PROBLEMS; MATHEMATICAL MANIFOLDS; SPACE

Citation Formats

Dumanyan, Vagram Zh. Solvability of the Dirichlet problem for a general second-order elliptic equation. United States: N. p., 2011. Web. doi:10.1070/SM2011V202N07ABEH004174; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Dumanyan, Vagram Zh. Solvability of the Dirichlet problem for a general second-order elliptic equation. United States. doi:10.1070/SM2011V202N07ABEH004174; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Dumanyan, Vagram Zh. Sun . "Solvability of the Dirichlet problem for a general second-order elliptic equation". United States. doi:10.1070/SM2011V202N07ABEH004174; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21592532,
title = {Solvability of the Dirichlet problem for a general second-order elliptic equation},
author = {Dumanyan, Vagram Zh},
abstractNote = {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.},
doi = {10.1070/SM2011V202N07ABEH004174; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 7,
volume = 202,
place = {United States},
year = {2011},
month = {7}
}