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About the Lamé system in a polygonal or a polyhedral domain and a coupled problem between the Lamé system and the plate equation. I: Regularity of the solutions. (English) Zbl 0782.73041

The first part of the series of two papers is devoted to the studies of the regularity of the solutions of non-homogeneous mixed boundary value problem for the Lamé system in the polyhedral domain in \(\mathbb{R}^ 3\). Even if the transformation to the homogeneous boundary conditions by means of the trace theorem is impossible (the racracked domains are allowed), the results concerning vertex and edge singularities are reestablished, but only with a regularity \(H^{3/2+\varepsilon}\) (for some \(\varepsilon>0)\) of a regular part. Then, the sufficient geometrical conditions on the domain, which ensure the \(H^{3/2+\varepsilon}\)-regularity for the weak solutions, are given.
The author applies these new theoretical results to the solution of a problem coupling the linear elasticity system in the unit cube in \(\mathbb{R}^ 3\) with a plane racrack and the plate equation on a plane domain.
Reviewer: O.John (Praha)

MSC:

74K20 Plates
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
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References:

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