1. Estimates of the principal eigenvalue of the p-Laplacian and the p-biharmonic operator
- Creator:
- Benedikt, Jiří
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- eigenvalue problem for p-Laplacian, eigenvalue problem for p-biharmonic operator, estimates of principal eigenvalue, and asymptotic analysis
- Language:
- English
- 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)).
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public