## On the Dirichlet problem in elasticity for a domain exterior to an arc.(English)Zbl 0742.73026

The Dirichlet problem for the two-dimensional linear elasticity in the domain exterior to an open arc in the plane is considered. The problem is reduced to a system of boundary integral equations with the unknown density function being the jump of stresses across the arc. Existence, uniqueness and regularity conditions are established in appropriate Sobolev spaces. The asymptotic expansions concerning the singular behaviour for the solution near the tips of the arc are obtained. An augmented Galerkin procedure is used for the corresponding boundary integral equations to obtain a quasi-optimal rate of convergence for the approximate solutions.

### MSC:

 74S15 Boundary element methods applied to problems in solid mechanics 74B99 Elastic materials 74H99 Dynamical problems in solid mechanics 65N38 Boundary element methods for boundary value problems involving PDEs 35B65 Smoothness and regularity of solutions to PDEs 74R99 Fracture and damage 35C20 Asymptotic expansions of solutions to PDEs
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### References:

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