Analysis of Boundary-Domain Integral Equations for Variable Coefficient (The Case of Dirichelet Bvp in 2d)
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Date
2017-06
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Addis Ababa University
Abstract
Using an appropriate parametrix (Levi function), Dirichlet boundary value problem is reduced
to some direct segregated systems of Boundary- Domain Integral Equations (BDIEs).
Although the theory of BDIEs in 3D is well developed, the BDIEs in 2D need a special
consideration due to their different equivalence properties. Consequently, we need
to set conditions on the domain or the spaces to insure the invertibility of corresponding
parametrix-based integral layer potentials and hence the unique solubility of BDIEs.
The properties of corresponding potential operators are investigated. The equivalence of
the original BVP and the obtained BDIEs are analysed and the invertibility of the BDIE
operators is proved.
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Keywords
Analysis of Boundary-Domain Integral, Equations for Variable Coefficient