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

Alberto Cialdea, Vita Leonessa and Angelica Malaspina

Abstract and Applied Analysis, 2015, vol. 2015, issue 1

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 Rm (m ≥ 3) 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.

Date: 2015
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https://doi.org/10.1155/2015/276810

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:276810

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