T. G. Ayele, S. E. Mikhailov, “Analysis of two-operator boundary-domain integral equations for variable-coefficient mixed BVP”, Eurasian Math. J., 2011, Volume 2, Number 3,Pages <nobr>20

This article is cited in 7 papers

Analysis of two-operator boundary-domain integral equations for variable-coefficient mixed BVP

T. G. Ayele^a, S. E. Mikhailov^b

^a Department of Mathematics, Addis Ababa University, Addis Ababa, Ethiopia
^b Department of Mathematical Science, Brunel University London, Uxbridge, UK

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.

Keywords and phrases: partial differential equations, variable coefficients, parametrix, boundary-domain integral equations, equivalence, unique solvability and invertibility.

MSC: 35J25, 31B10, 45P05, 45A05, 47G10, 47G30, 47G40

Received: 07.03.2011

Language: English