Mixed Crack Type Problem in Anisotropic Elasticity

The paper deals with three‐dimensional mixed boundary value problem of the anisotropic elasticity theory when the elastic body under consideration has a cut in the form of an arbitrary non‐closed, two‐dimensional, smooth surface with a smooth boundary: on one side of the cut surface the Dirichlet ty...

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Bibliographic Details
Published in:Mathematische Nachrichten 1998, Vol.191 (1), p.83-107
Main Authors: Duduchava, R., Natroshvili, D.
Format: Article
Language:English
Subjects:
Anisotropic elasticity
asymptotics
mixed boundary conditions
potential method
pseudodifferential equations
regularity of solutions
uniqueness theorems
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Summary:The paper deals with three‐dimensional mixed boundary value problem of the anisotropic elasticity theory when the elastic body under consideration has a cut in the form of an arbitrary non‐closed, two‐dimensional, smooth surface with a smooth boundary: on one side of the cut surface the Dirichlet type condition (i.e., the displacement vector) is given, while on the other side the Neumann type condition (i.e., the stress vector) is prescribed. Applying the potential method and invoking the theory of ΨDEs uniqueness, existence and regularity results are proved in various function spaces. The asymptotic expansion of the solution of the corresponding system of boundary ΨDEs is written.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.19981910105