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http://bura.brunel.ac.uk/handle/2438/16657
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. |
URI: | https://bura.brunel.ac.uk/handle/2438/16657 |
DOI: | http://dx.doi.org/10.1186/s13661-018-0992-0 |
ISSN: | 1687-2762 1687-2770 |
Appears in Collections: | Dept of Mathematics Research Papers |
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Fulltext.pdf | 1.93 MB | Adobe PDF | View/Open |
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