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

Alberto Cialdea, Vita Leonessa, Angelica Malaspina

Type: Article

Publication Date: 2015-01-01

Citations: 7

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

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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>m</mml:mi><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:math>) 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.

Locations

Project Euclid (Cornell University) - View - PDF
DOAJ (DOAJ: Directory of Open Access Journals) - View
CINECA IRIS Institutional Research Information System (University of Basilicata) - View - PDF
Abstract and Applied Analysis - View - PDF

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+	The Simple-Layer Potential Approach to the Dirichlet Problem: An Extension to Higher Dimensions of Muskhelishvili Method and Applications	2017	Alberto Cialdea
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+	On the double layer potential ansatz for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math>-dimensional Helmholtz equation with Neumann condition	2020	Alberto Cialdea Vita Leonessa Angelica Malaspina
+ PDF Chat	On the traction problem for steady elastic oscillations equations: the double layer potential ansatz	2022	Alberto Cialdea Vita Leonessa Angelica Malaspina
+	Some New Applications of the Theory of Conjugate Differential Forms	2019	Alberto Cialdea

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+	Singular Integral Operators	1986	Solomon G. Mikhlin Siegfried Prößdorf
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