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A mixed boundary value problem for the partial differential equation ofdiffusion in an inhomogeneous medium in a Lipschitz domain is reduced to asystem of direct segregated parametrix-based Boundary-Domain Integral Equations(BDIEs). We use a parametrix different from the one employed in the papers byMikhailov (2002, 2006) and Chkadua, Mikhailov, Natroshvili (2009). We prove theequivalence between the original BVP and the corresponding BDIE system. Theinvertibility and Fredholm properties of the boundary-domain integral operatorsare also analysed.

the journal of integral equations and applications/journal of integral equations and applications

Analysis of Boundary-Domain Integral Equations based on a new parametrix  for the mixed diffusion BVP with variable coefficient in an interior  Lipschitz domain