Integral representations for solutions of some BVPs for the Lamé system in multiply connected domains
Department of Mathematics and Computer Science, University of Basilicata, V.le dell'Ateneo Lucano, 10, Campus of Macchia Romana, 85100 Potenza, Italy
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.