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Title: Analysis of segregated boundary-domain integral equations for BVPs with non-smooth coefficients on Lipschitz domains
Authors: Mikhailov, SE
Keywords: Partial differential equations;Non-smooth coefficients;Sobolev spaces;Parametrix;Integral equations;Equivalence
Issue Date: 2018
Publisher: SpringerOpen
Citation: Boundary Value Problems, 2018, 2018 (1)
Abstract: Segregated direct boundary-domain integral equations (BDIEs) based on a parametrix and associated with the Dirichlet and Neumann boundary value problems for the linear stationary diffusion partial differential equation with a variable Hölder-continuous coefficients on Lipschitz domains are formulated. The PDE right-hand sides belong to the Sobolev (Bessel potential) space Hs−2(Ω ) or H˜s−2(Ω ) , 12<s<32, when neither strong classical nor weak canonical co-normal derivatives are well defined. Equivalence of the BDIEs to the original BVP, BDIE solvability, solution uniqueness/non-uniqueness, and the Fredholm property and invertibility of the BDIE operators are analysed in appropriate Sobolev spaces. It is shown that the BDIE operators for the Neumann BVP are not invertible; however, some finite-dimensional perturbations are constructed leading to invertibility of the perturbed (stabilised) operators.
ISSN: 1687-2762
Appears in Collections:Dept of Mathematics Research Papers

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