On the eigenvalues of a Robin problem with a large parameter

Title:

On the eigenvalues of a Robin problem with a large parameter

Creator:

Filinovskiy, Alexey

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8f6a885b-2899-465c-95ea-76379f2a1fe2
uuid:8f6a885b-2899-465c-95ea-76379f2a1fe2
doi:10.21136/MB.2014.143859

Subject:

Laplace operator, Robin boundary condition, eigenvalue, and large parameter

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We consider the Robin eigenvalue problem ∆u + λu = 0 in Ω, ∂u/∂ν + αu = 0 on ∂Ω where Ω ⊂ R n , n > 2 is a bounded domain and α is a real parameter. We investigate the behavior of the eigenvalues λk(α) of this problem as functions of the parameter α. We analyze the monotonicity and convexity properties of the eigenvalues and give a variational proof of the formula for the derivative λ ′ 1 (α). Assuming that the boundary ∂Ω is of class C 2 we obtain estimates to the difference λ D k −λk(α) between the k-th eigenvalue of the Laplace operator with Dirichlet boundary condition in Ω and the corresponding Robin eigenvalue for positive values of α for every k = 1, 2, . . ..

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

341-352

Source:

Mathematica bohemica | 2014 Volume:139 | Number:2

Harvested from:

CDK

Metadata only:

false