In this paper the work of Berestycki, Nirenberg and Varadhan on the maximum principle and the principal eigenvalue for second order operators on general domains is extended to Riemannian manifolds. In particular it is proved that the refined maximum principle holds for a second order elliptic operat
Inequalities for eigenvalues of elliptic operators in divergence form on Riemannian manifolds
โ Scribed by Manfredo P. do Carmo; Qiaoling Wang; Changyu Xia
- Publisher
- Springer
- Year
- 2010
- Tongue
- English
- Weight
- 212 KB
- Volume
- 189
- Category
- Article
- ISSN
- 0373-3114
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold of positive scalar curvature admitting a parallel one-form is found. The possible universal covering spaces of the manifolds on which the smallest possible eigenvalue is attained are also listed. Moreover,
## Abstract We study the asymptotic behavior of the eigenvalues and the eigenfunctions of the LaplaceโBeltrami operator on a Riemannian manifold __M__^ฮต^ depending on a small parameter ฮต>0 and whose structure becomes complicated as ฮตโ0. Under a few assumptions on scales of __M__^ฮต^ we obtain the ho