The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz-Reference-Cited by-同舟云学术

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

Published:2015 Issue: Volume:2015 Page:1-11
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Cialdea Alberto¹^ORCID,Leonessa Vita¹^ORCID,Malaspina Angelica¹^ORCID

Affiliation:

1. Department of Mathematics, Computer Science and Economics, University of Basilicata, Viale dell'Ateneo Lucano 10, 85100 Potenza, Italy

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 ofRm(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.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2015/276810.pdf

Reference19 articles.

1. Analysis of segregated boundary-domain integral equations for variable-coefficient problems with cracks

2. Localized Boundary-Domain Singular Integral Equations Based on Harmonic Parametrix for Divergence-Form Elliptic PDEs with Variable Matrix Coefficients

3. Boundary Integral Equations

4. Poisson problems for semilinear Brinkman systems on Lipschitz domains in $${\mathbb{R}^n}$$ R n

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On the traction problem for steady elastic oscillations equations: the double layer potential ansatz;Rendiconti del Circolo Matematico di Palermo Series 2;2022-07-04

2. On the double layer potential ansatz for the n-dimensional Helmholtz equation with Neumann condition;Electronic Journal of Qualitative Theory of Differential Equations;2020

3. On the Simple Layer Potential Ansatz for the n-Dimensional Helmholtz Equation;Applied and Numerical Harmonic Analysis;2020

4. Some New Applications of the Theory of Conjugate Differential Forms;Trends in Mathematics;2019

5. On Indirect Boundary Integral Equation Methods and Applications;Trends in Mathematics;2019