Estimate of the spectrum deviation of the singularly perturbed Steklov problem
- Authors: Chechkina A.G.1
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Affiliations:
- Mechanics and Mathematics Faculty
- Issue: Vol 96, No 2 (2017)
- Pages: 510-513
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225405
- DOI: https://doi.org/10.1134/S1064562417050301
- ID: 225405
Cite item
Abstract
A Steklov-type problem with rapidly alternating Dirichlet and Steklov boundary conditions in a bounded n-dimensional domain in considered. The regions on which the Steklov condition is given have diameter of order ε, and the distance between them is larger than or equal to 2ε. It is proved that, as the small parameter tends to zero, the eigenvalues of this problem degenerate, i.e., tend to infinity. It is also proved that the rate of increase to infinity is larger than or equal to |ln ε|δ, δ ∈ (0;2 − 2/n) as ε, tends to zero.
About the authors
A. G. Chechkina
Mechanics and Mathematics Faculty
Author for correspondence.
Email: chechkina@gmail.com
Russian Federation, Moscow, 119991