Integral representations for solutions of some BVPs for the Lamé system in multiply connected domains
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Boundary Value Problems 2011, 2011:53 doi:10.1186/1687-2770-2011-53Published: 12 December 2011
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.