Geodesic
Analysis of two-operator boundary-domain integral equations for variable-coefficient mixed BVP
Eurasian mathematical journal, Tome 2 (2011) no. 3, pp. 20-41.

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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. 
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T. G. Ayele; S. E. Mikhailov. Analysis of two-operator boundary-domain integral equations for variable-coefficient mixed BVP. Eurasian mathematical journal, Tome 2 (2011) no. 3, pp. 20-41. http://geodesic.mathdoc.fr/item/EMJ_2011_2_3_a1/

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