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2024 | OriginalPaper | Chapter

Efficient Construction Technique for Resolving Dirichlet Boundary-Value Problems in Multiply Connected Domains for Real Elliptic Equations

Author : Ahmad Qazza

Published in: Mathematical Analysis and Numerical Methods

Publisher: Springer Nature Singapore

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Abstract

This paper introduces a novel analytic approach for solving Dirichlet boundary-value problems for regular solutions of second-order elliptic differential equations. The methodology uses complex variables \(z=x+iy\) and \(\zeta =x-iy\) and integral representation techniques for regular solutions within the multiply connected domain \(T\). The regular solution is represented as \(\text{Re} U(z, \zeta )\) satisfying the symmetry condition \(U(\overline{\zeta }, \overline{z } ) = \stackrel{-}{(U(z, \zeta ))}\). This approach extends its applicability beyond domains bounded by Lyapunov and Vekua and provides efficient resolutions for Dirichlet boundary-value problems in multiply connected domains for real elliptic equations.

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Title: Efficient Construction Technique for Resolving Dirichlet Boundary-Value Problems in Multiply Connected Domains for Real Elliptic Equations
Author: Ahmad Qazza
Publisher: Springer Nature Singapore
Book: Mathematical Analysis and Numerical Methods
Print ISBN: 978-981-9748-75-4

Electronic ISBN: 978-981-9748-76-1

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-981-97-4876-1_29

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