On the Resolvent of Multidimensional Operators with Frequently Alternating Boundary Conditions with the Robin Homogenized Condition
- Авторлар: Borisov D.1,2,3, Sharapov T.2
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Мекемелер:
- Institute of Mathematics, USC RAS
- Bashkir State Pedagogical University
- University of Hradec Králové
- Шығарылым: Том 213, № 4 (2016)
- Беттер: 461-503
- Бөлім: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237196
- DOI: https://doi.org/10.1007/s10958-016-2720-6
- ID: 237196
Дәйексөз келтіру
Аннотация
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.
Авторлар туралы
D. Borisov
Institute of Mathematics, USC RAS; Bashkir State Pedagogical University; University of Hradec Králové
Хат алмасуға жауапты Автор.
Email: borisovdi@yandex.ru
Ресей, 112, Chernyshevskii St., Ufa, 450008; 3a, October Revolution St., Ufa, 450000; 62, Rokitanského, Hradec Králové, 50003
T. Sharapov
Bashkir State Pedagogical University
Email: borisovdi@yandex.ru
Ресей, 3a, October Revolution St., Ufa, 450000