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Integral representations for solutions of some BVPs for the Lamé system in multiply connected domains

Alberto Cialdea*, Vita Leonessa and Angelica Malaspina

Author affiliations

Department of Mathematics and Computer Science, University of Basilicata, V.le dell'Ateneo Lucano, 10, Campus of Macchia Romana, 85100 Potenza, Italy

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Citation and License

Boundary Value Problems 2011, 2011:53  doi:10.1186/1687-2770-2011-53

Published: 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.

Lamé system; boundary integral equations; potential theory; differential forms; multiply connected domains