On estimation of the logarithmic Sobolev constant and gradient estimates of heat semigroups
β Scribed by Feng-Yu Wang
- Publisher
- Springer
- Year
- 1997
- Tongue
- English
- Weight
- 182 KB
- Volume
- 108
- Category
- Article
- ISSN
- 1432-2064
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π SIMILAR VOLUMES
We give a new proof of the following inequality. In any dimension n G 2 and for Ε½ . 1-p-nlet s s n q p r2 p. Then p, s Ε½ n . where L R denotes the usual Sobolev space and ΩΒ¨denotes the gradient of The choice of s is optimal, as is the requirement that n ) p. In addition, some Sobolev norms of u ΩΒ¨
## Abstract In this paper a number of explicit lower bounds are presented for the first Neumann eigenvalue on nonβconvex manifolds. The main idea to derive these estimates is to make a conformal change of the metric such that the manifold is convex under the new metric, which enables one to apply k