On Davies’ conjecture and strong ratio limit properties for the heat kernel. (English) Zbl 1116.58027

Aikawa, Hiroaki (ed.) et al., Potential theory in Matsue. Selected papers of the international workshop on potential theory, Matsue, Japan, August 23–28, 2004. Tokyo: Mathematical Society of Japan (ISBN 4-931469-33-7/hbk). Advanced Studies in Pure Mathematics 44, 339-352 (2006).
The author studies strong ratio limit properties and the exact long time asymptotics for the heat kernel of a general second order parabolic operator with real Hölder coefficients defined on a compact Riemannian manifold.
For the entire collection see [Zbl 1102.31001].


58J35 Heat and other parabolic equation methods for PDEs on manifolds
35K10 Second-order parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
60J60 Diffusion processes
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