Analysis of Direct Segregated Boundary- Domain Integral Equations for Variable-Coefficient Mixed Bvps in Exterior Domains
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Date
2012-02
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Addis Ababa University
Abstract
Direct segregated systems of boundary-domain integral equations are formulated from the mixed
(Dirichlet-Neumann) boundary value problems for a scalar second order divergent elliptic partial
differential equation with a variable coefficient in an exterior three-dimensional domain.
The boundary-domain integral equation system equivalence to the original boundary value problems
and the Fredholm properties and invertibility of the corresponding boundary-domain integral operators
are analyzed in weighted Sobolev spaces suitable for infinite domains. This analysis is based on the
corresponding properties of the BVPs in Weighted Sobolev spaces that are proved as well.
Key words:
Partial Differential Equation; Variable coefficient; Mixed problem; Parametrix; Levi function;
Boundary-domain integral equations: Unbounded domain; Weighted Sobolev spaces.
Description
Keywords
Partial Differential Equation, Variable Coefficient, Mixed Problem, Parametrix, Levi Function, Boundary-Domain Integral Equations, Unbounded Domain, Weighted Sobolev Spaces