Existence and Uniqueness of an Rν-Generalized Solution of the Dirichlet Problem for the Lamé System with a Corner Singularity

We consider the Dirichlet problem for the Lamé system in a two-dimensional domain whose boundary contains a reentrant corner. The notion of R v -generalized solution is introduced for this problem. The existence and uniqueness of such a solution in the weighted set W ∘ 2 , v ∗ 1 ( Ω , δ ) is proved....

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Bibliographic Details
Published in:	Differential equations Vol. 55; no. 6; pp. 832 - 840
Main Authors:	Rukavishnikov, V. A., Rukavishnikova, E. I.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01-06-2019 Springer Nature B.V
Subjects:	Difference and Functional Equations Differential equations Dirichlet problem Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Uniqueness
Online Access:	Get full text
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Summary:	We consider the Dirichlet problem for the Lamé system in a two-dimensional domain whose boundary contains a reentrant corner. The notion of R v -generalized solution is introduced for this problem. The existence and uniqueness of such a solution in the weighted set W ∘ 2 , v ∗ 1 ( Ω , δ ) is proved.
ISSN:	0012-2661 1608-3083
DOI:	10.1134/S0012266119060107