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The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz

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  • Alberto Cialdea
  • Vita Leonessa
  • Angelica Malaspina

Abstract

We investigate the Dirichlet problem related to linear elliptic second-order partial differential operators with smooth coefficients in divergence form in bounded connected domains of ( ) with Lyapunov boundary. In particular, we show how to represent the solution in terms of a simple layer potential. We use an indirect boundary integral method hinging on the theory of reducible operators and the theory of differential forms.

Suggested Citation

  • Alberto Cialdea & Vita Leonessa & Angelica Malaspina, 2015. "The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-11, December.
    • Handle: RePEc:hin:jnlaaa:276810
    DOI: 10.1155/2015/276810
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