Asymptotics of eigenvalues of the Dirichlet problem in a thin domain. (English. Russian original) Zbl 0664.35064

Nazarov, S. A.

Sov. Math. 31, No. 11, 68-80 (1987); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1987, No. 11(306), 54-64 (1987).

The paper is concerned with the asymptotics of some eigenvalues \(\lambda\) (\(\epsilon)\) as \(\epsilon\) \(\to 0\) of elliptic second-order differential operators in a cylinder with a height \(\epsilon\) and with Dirichlet boundary conditions. The author describes the first two terms in the asymptotics.

Reviewer: G.Popov

MSC:

35P20	Asymptotic distributions of eigenvalues in context of PDEs
35J25	Boundary value problems for second-order elliptic equations

Keywords:

asymptotics; eigenvalues; Dirichlet boundary conditions