Localized Boundary-domain Integral Equations For Dirichlet Problem For Second Order Elliptic Equations With Matrix Variable Coefficients

Employing a localized parametrix the Dirichlet boundary value problem for elliptic equations in the divergence form with general variable matrix coefficients is reduced to localized boundary domain integral equations (LBDIE) system. The Levi function given in the paper is checked The equivalence between the Dirichlet problem and the LBDIE system is studied. It is established that the localized boundary domain integral operator obtained in the paper belongs to the Boutet De Monvel algebra and the operator Fredholm properties and invertibility is investigated by the Wiener-Hopf factorization method

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