Eigenvalues of the Laplacian in a Disk with the Dirichlet Condition on Finitely Many Small Boundary Parts in the Critical Case
- Авторы: Gadyl’shin R.1,2, Rep’evskii S.3, Shishkina E.1
-
Учреждения:
- M. Akmullah Bashkir State Pedagogical University
- Bashkir State University
- Chelyabinsk State University
- Выпуск: Том 213, № 4 (2016)
- Страницы: 510-529
- Раздел: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237200
- DOI: https://doi.org/10.1007/s10958-016-2722-4
- ID: 237200
Цитировать
Аннотация
We consider the boundary value problem for eigenvalues of the negative Laplace operator in a disk with the Neumann boundary condition on the circle except for finitely many (more than 1) small arcs, where the Dirichlet boundary condition is imposed, with lengths tending to zero. We construct complete asymptotics expansions of egenvalues with respect to the parameter (the arc length) converging to a double eigenvalue to the limit Neumann problem, in the critical case, where one of the eigenfunctions of the limit problem vanishes at all contraction points for small arcs.
Об авторах
R. Gadyl’shin
M. Akmullah Bashkir State Pedagogical University; Bashkir State University
Автор, ответственный за переписку.
Email: gadylshin@yandex.ru
Россия, 3a, Oktyabrskoy Revolutsii St., Ufa, 450000; 32, Frunze st., Ufa, 450074
S. Rep’evskii
Chelyabinsk State University
Email: gadylshin@yandex.ru
Россия, 129, Brat’ev Kashirinykh St., Chelyabinsk, 454000
E. Shishkina
M. Akmullah Bashkir State Pedagogical University
Email: gadylshin@yandex.ru
Россия, 3a, Oktyabrskoy Revolutsii St., Ufa, 450000