Email this article On the Resolvent of Multidimensional Operators with Frequently Alternating Boundary Conditions with the Robin Homogenized Condition
- Authors: Borisov D.I.1,2,3, Sharapov T.F.2
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Affiliations:
- Institute of Mathematics, USC RAS
- Bashkir State Pedagogical University
- University of Hradec Králové
- Issue: Vol 213, No 4 (2016)
- Pages: 461-503
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237196
- DOI: https://doi.org/10.1007/s10958-016-2720-6
- ID: 237196
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Abstract
We consider an elliptic operator in a multidimensional domain with frequent alternation of the Dirichlet condition and the Robin boundary condition in the case where the homogenized operator contains only the original Robin boundary condition. We prove the uniform resolvent convergence of the perturbed operator to the homogenized operator and obtain order sharp estimates for the rate of convergence. We construct a complete asymptotic expansion for the resolvent in the case where the resolvent acts on sufficiently smooth functions and the alternation of boundary conditions is strictly periodic and is given on a multidimensional hyperplane. Bibliography: 23 titles.
About the authors
D. I. Borisov
Institute of Mathematics, USC RAS; Bashkir State Pedagogical University; University of Hradec Králové
Author for correspondence.
Email: borisovdi@yandex.ru
Russian Federation, 112, Chernyshevskii St., Ufa, 450008; 3a, October Revolution St., Ufa, 450000; 62, Rokitanského, Hradec Králové, 50003
T. F. Sharapov
Bashkir State Pedagogical University
Email: borisovdi@yandex.ru
Russian Federation, 3a, October Revolution St., Ufa, 450000
