Analysis Of Direct Segregated Boundary- Domain Integral Equations For Variable-coefficient Mixed Bvps In Exterior Domains

Direct segregated systems of boundary-domain integral equations are formulated from the mixedrn(Dirichlet-Neumann) boundary value problems for a scalar second order divergent elliptic partialrndifferential equation with a variable coefficient in an exterior three-dimensional domain.rnThe boundary-domain integral equation system equivalence to the original boundary value problemsrnand the Fredholm properties and invertibility of the corresponding boundary-domain integral operatorsrnare analyzed in weighted Sobolev spaces suitable for infinite domains. This analysis is based on therncorresponding properties of the BVPs in Weighted Sobolev spaces that are proved as well.rnKey words:rnPartial Differential Equation; Variable coefficient; Mixed problem; Parametrix; Levi function;rnBoundary-domain integral equations: Unbounded domain; Weighted Sobolev spaces.

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