Abstract
The present paper is concerned with an indirect method to solve the Dirichlet and the traction problems for Lamé system in a multiply connected bounded domain of ℝn, n ≥ 2. It hinges on the theory of reducible operators and on the theory of differential forms. Differently from the more usual approach, the solutions are sought in the form of a simple layer potential for the Dirichlet problem and a double layer potential for the traction problem.2000 Mathematics Subject Classification. 74B05; 35C15; 31A10; 31B10; 35J57.
Highlights
In this paper we consider the Dirichlet and the traction problems for the linearized ndimensional elastostatics
The classical indirect methods for solving them consist in looking for the solution in the form of a double layer potential and a simple layer potential respectively
It is well-known that, if the boundary is sufficiently smooth, in both cases we are led to a singular integral system which can be reduced to a Fredholm one
Summary
In this paper we consider the Dirichlet and the traction problems for the linearized ndimensional elastostatics. It is well-known that, if the boundary is sufficiently smooth, in both cases we are led to a singular integral system which can be reduced to a Fredholm one (see, e.g., [1]) This approach was considered in multiply connected domains for several partial differential equations (see, e.g., [2,3,4,5,6,7]). Another one consists in looking for the solution of the Dirichlet problem in the form of a simple layer potential This approach leads to an integral equation of the first kind on the boundary which can be treated in different ways. Where [LyΓ(x, y)]’ denotes the transposed matrix of Ly[Γ(x, y)]
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