Solvability of some overdetermined elliptic system in a domain with corners π/n
作者:
W. M. Zajaczkowski,
A. Piskorek,
期刊:
Mathematical Methods in the Applied Sciences
(WILEY Available online 1982)
卷期:
Volume 4,
issue 1
页码: 15-18
ISSN:0170-4214
年代: 1982
DOI:10.1002/mma.1670040103
出版商: John Wiley&Sons, Ltd
数据来源: WILEY
摘要:
AbstractIn the paper we prove the existence and uniqueness of solutions of the overdetermined elliptic system\documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {\left( {\rm A} \right)} & {{\rm rot }\upsilon {\rm = }\omega } & {{\rm div }\upsilon {\rm = 0}} & {\upsilon \cdot {\rm }\bar n|_{\partial \Omega } = b} \\ \end{array} $$\end{document}whereb, ω are given functions, in a domain ΩCR3with corners π/n, n= 2, 3, … The proof is divided on two steps, we construct a solution for the Laplace equation in a dihedral angle π/n, using the method of reflection and we get an estimate in the norms of the Sobolev spaces in some neighbourhood of the edge. In the dihedral angle system (A) reduces to the Dirichlet and Neumann problems for the Laplace equation. In the next step we prove the existence of solutions in the Sobolev spacesWpl(Ω) using the existence of generalized solutions
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