Estimates of the principal eigenvalue of the p-Laplacian and the p-biharmonic operator

Title:

Estimates of the principal eigenvalue of the p-Laplacian and the p-biharmonic operator

Creator:

Benedikt, Jiří

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:da3ede32-0d41-4359-b868-28e1a1ce503b
uuid:da3ede32-0d41-4359-b868-28e1a1ce503b
doi:10.21136/MB.2015.144327

Subject:

eigenvalue problem for p-Laplacian, eigenvalue problem for p-biharmonic operator, estimates of principal eigenvalue, and asymptotic analysis

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We survey recent results concerning estimates of the principal eigenvalue of the Dirichlet p-Laplacian and the Navier p-biharmonic operator on a ball of radius R in R N and its asymptotics for p approaching 1 and ∞. Let p tend to ∞. There is a critical radius RC of the ball such that the principal eigenvalue goes to ∞ for 0 < R 6 RC and to 0 for R > RC . The critical radius is RC = 1 for any N ∈ N for the p-Laplacian and RC = √ 2N in the case of the p-biharmonic operator. When p approaches 1, the principal eigenvalue of the Dirichlet p-Laplacian is NR−1 × (1− (p − 1) log R(p − 1)) + o(p − 1) while the asymptotics for the principal eigenvalue of the Navier p-biharmonic operator reads 2N/R2 + O(−(p − 1) log(p − 1)).

Language:

English

Rights:

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

Coverage:

215-222

Source:

Mathematica bohemica | 2015 Volume:140 | Number:2

Harvested from:

CDK

Metadata only:

false