ANALYSIS OF TWO-OPERATOR BOUNDARY-DOMAIN INTEGRAL EQUATIONS FOR VARIABLE-COEFFICIENT MIXED BVP

Abstract

Applying the two-operator approach, the mixed (Dirichlet-Neumann) boundary value problem for a second-order scalar elliptic differential equation with variable coefficients is reduced to several systems of Boundary Domain Integral Equations, briefly BDIEs. The two-operator BDIE system equivalence to the boundary value problem, BDIE solvability and the invertibility of the boundary-domain integral operators are proved in the appropriate Sobolev spaces.