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2019 | OriginalPaper | Chapter

Boundary-Domain Integral Equations for Variable Coefficient Dirichlet BVP in 2D Unbounded Domain

Authors : T. T. Dufera, S. E. Mikhailov

Published in: Analysis, Probability, Applications, and Computation

Publisher: Springer International Publishing

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Abstract

In this paper, the Dirichlet boundary value problem for the second order stationary diffusion elliptic partial differential equation with variable coefficient is considered in unbounded (exterior) two-dimensional domain. Using an appropriate parametrix (Levi function), this problem is reduced to some direct segregated boundary-domain integral equations (BDIEs). We investigate the properties of corresponding parametrix-based integral volume and layer potentials in some weighted Sobolev spaces, as well as the unique solvability of BDIEs and their equivalence to the original BVP.

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previous chapter Analysis of Boundary-Domain Integral Equations for Variable-Coefficient Mixed BVP in 2D
next chapter A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients
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Metadata
Title
Boundary-Domain Integral Equations for Variable Coefficient Dirichlet BVP in 2D Unbounded Domain
Authors
T. T. Dufera
S. E. Mikhailov
Copyright Year
2019
Book
Analysis, Probability, Applications, and Computation

Print ISBN: 978-3-030-04458-9

Electronic ISBN: 978-3-030-04459-6

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-04459-6_46

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