## Abstract We study the asymptotic behavior of the eigenvalues and the eigenfunctions of the Laplace–Beltrami operator on a Riemannian manifold __M__^ε^ depending on a small parameter ε>0 and whose structure becomes complicated as ε→0. Under a few assumptions on scales of __M__^ε^ we obtain the ho
✦ LIBER ✦
Global Comparison Principles for thep-Laplace Operator on Riemannian Manifolds
✍ Scribed by Ilkka Holopainen; Stefano Pigola; Giona Veronelli
- Publisher
- Springer Netherlands
- Year
- 2010
- Tongue
- English
- Weight
- 364 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0926-2601
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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