Analysis of Some Localized Boundary–Domain Integral Equations for Transmission Problems with Variable Coefficients

  • O. Chkadua
  • S. E. Mikhailov
  • D. Natroshvili


Some segregated systems of direct localized boundary-domain integral equations (LBDIEs) associated with several transmission problems for scalar PDEs with variable coefficients are formulated and analyzed for a bounded domain composed of two subdomains with a coefficient jump over the interface. The main results established in the paper are the LBDIE equivalence to the original transmission problems and the invertibility of the corresponding localized boundary-domain integral operators in corresponding Sobolev spaces function spaces.


Localize Potential Transmission Problem Equivalence Theorem Green Identity Local Boundary Integral Equation 
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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.A.Razmadze Mathematical InstituteTbilisiGeorgia
  2. 2.Brunel University West LondonUxbridgeUK
  3. 3.Georgian Technical UniversityTbilisiGeorgia

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