Analysis of segregated boundary-domain integral equations for variable-coefficient problems with cracks

This is the pre-print version of the article. The official published version can be obtained from the link below - Copyright @ 2011 Wiley-BlackwellSegregated direct boundary-domain integral equation (BDIE) systems associated with mixed, Dirichlet and Neumann boundary value problems (BVPs) for a scalar “Laplace” PDE with variable coefficient are formulated and analyzed for domains with interior cuts (cracks). The main results established in the paper are the BDIE equivalence to the original BVPs and invertibility of the BDIE operators in the corresponding Sobolev spaces.This work was supported by the International Joint Project Grant - 2005/R4 ”Boundary- Domain Integral Equations: Formulation, Analysis, Localisation” of the Royal Society, UK, and the grant ”Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients” of the EPSRC, UK