Analysis of direct boundary-domain integral equations for a mixed bvp with variable coefficient, i: Equivalence and invertibility

Abstract

A mixed (Dirichlet-Neumann) boundary val-ue problem (BVP) for the "stationary heat transfer" par-tial differential equation with variable coefficient is reduced to some systems of nonstandard segregated direct paramet-rix-based boundary-domain integral equations (BDIEs). The BDIE systems contain integral operators denned on the do-main under consideration as well as potential-type and pseudo-differential operators denned on open submanifolds of the boundary. It is shown that the BDIE systems are equivalent to the original mixed BVP, and the operators of the BDIE systems are invertible in appropriate Sobolev spaces. © 2009 Rocky Mountain Mathematics Consortium.