Solution of the Dirichlet Problem for the Inhomogeneous Lamé System with Lower Order Coefficients

We consider the Dirichlet problem for the inhomogeneous Lamé system in the plane with constant leading coefficients in a (finite or infinite) domain, bounded by a Lyapunov contour. For domains of finite diameter we use the weighted Hölder class of functions with power behavior at infinity. We propos...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2021-06, Vol.255 (6), p.732-740
Main Authors: Mitin, S. P., Soldatov, A. P.
Format: Article
Language:English
Subjects:
Contours
Dirichlet problem
Domains
Fredholm equations
Integral equations
Mathematics
Mathematics and Statistics
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Summary:We consider the Dirichlet problem for the inhomogeneous Lamé system in the plane with constant leading coefficients in a (finite or infinite) domain, bounded by a Lyapunov contour. For domains of finite diameter we use the weighted Hölder class of functions with power behavior at infinity. We propose an equivalent reduction of the problem to a system of Fredholm integral equations in the domain and on the boundary contour.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05410-6