Rate of convergence of eigenvalues to singularly perturbed Steklov-type problem for elasticity system

ABSTRACT

In the paper, we study the Steklov-type problem for the system of elasticity with rapidly changing boundary condition depending on a small parameter $\mathit{\epsilon }$. We construct the homogenized (limit) problem and estimate the rate of convergence of the eigenvalues and eigenfunctions of the initial problem as $\mathit{\epsilon }\to 0$.

KEYWORDS:

• Homogenization
• rapidly changing boundary conditions
• Steklov-type problem
• elasticity system

AMS SUBJECT CLASSIFICATIONS:

• 35B27
• 35P05
• 74B05

Acknowledgements

The authors also want to thank the referee for interesting remarks and suggestions. This paper was mostly written during the stay of Aleksandra G. Chechkina at the Università degli Studi di Salerno in July 2017. She wants to express deep thanks for the hospitality, for wonderful conditions to work and for the support.

Notes

No potential conflict of interest was reported by the authors.

Dedicated to the bright memory of Vasilij Vasilievich Zhikov.

Additional information

Funding

The work of A.G.C. was partially supported by Russian Foundation for Basic Researches [project 15–01–07920]; Presidential Grant for the Support of Leading Scientific Schools [project HIII-7461.2016.1].