SHARP MODULUS OF CONTINUITY FOR PARABOLIC EQUATIONS ON MANIFOLDS AND LOWER BOUNDS FOR THE FIRST EIGENVALUE

被引：35
|
作者：
Andrews, Ben [1 ,2 ]
Clutterbuck, Julie [1 ]
机构：
[1] Australian Natl Univ, Inst Math Sci, Canberra, ACT 0200, Australia
[2] Tsinghua Univ, Ctr Math Sci, Beijing, Peoples R China
来源：
ANALYSIS & PDE | 2013年 / 6卷 / 05期
基金：
澳大利亚研究理事会;
关键词：
eigenvalue lower bound; heat equation; modulus of continuity; COMPACT; GAP;
D O I：
10.2140/apde.2013.6.1013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We derive sharp estimates on the modulus of continuity for solutions of the heat equation on a compact Riemannian manifold with a Ricci curvature bound, in terms of initial oscillation and elapsed time. As an application, we give an easy proof of the optimal lower bound on the first eigenvalue of the Laplacian on such a manifold as a function of diameter.
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页码：1013 / 1024
页数：12
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