  The paper deals with the three-dimensional Dirichlet boundary value problem
(BVP) for a second order strongly elliptic self-adjoint system of partial
differential equations in the divergence form with variable coefficients and
develops the integral potential method based on a localized parametrix. Using
Green's representation formula and properties of the localized layer and volume
potentials, we reduce the Dirichlet BVP to a system of localized
boundary-domain integral equations (LBDIEs). The equivalence between the
Dirichlet BVP and the corresponding LBDIE system is studied. We establish that
the obtained localized boundary-domain integral operator belongs to the Boutet
de Monvel algebra. With the help of the Wiener-Hopf factorization method we
investigate corresponding Fredholm properties and prove invertibility of the
localized operator in appropriate Sobolev (Bessel potential) spaces.
