Analysis of Direct Segregated Boundary- Domain Integral Equations for Variable-Coefficient Mixed Bvps in Exterior Domains

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Addis Ababa University


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.



Partial Differential Equation, Variable Coefficient, Mixed Problem, Parametrix, Levi Function, Boundary-Domain Integral Equations, Unbounded Domain, Weighted Sobolev Spaces