This article is cited in 5 papers

Asymptotics of Eigenvalues of the Two-Dimensional Dirichlet Boundary-Value Problem for the Lamé Operator in a Domain with a Small Hole

D. B. Davletov

Bashkir State Pedagogical University

Abstract: The Dirichlet boundary-value problem for the eigenvalues of the Lamé operator in a two-dimensional bounded domain with a small hole is studied. The asymptotics of the eigenvalue of this boundary-value problem is constructed and justified up to the power of the parameter defining the diameter of the hole.

Keywords: Dirichlet boundary-value problem, Lamé operator, Fredholm alternative, holomorphic function, asymptotics of eigenvalues, Bessel function.

UDC: 517.956

Received: 10.11.2010
Revised: 09.12.2011

DOI: 10.4213/mzm9023

 English version: Mathematical Notes, 2013, 93:4, 545–555

Bibliographic databases:

• 
• 
• 
• 
• 
•