On the heat kernel of a class of fourth order operators in two dimensions: Sharp Gaussian estimates and short time asymptotics

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Barbatis, G.¹  Branikas, P.¹ 

[1] Univ Athens, Dept Math, Athens 15784, Greece

关键词: Higher order parabolic equations;    Heat kernel estimates;    Short time asymptotics;   

DOI  :  10.1016/j.jde.2018.06.034

来源: Elsevier

【 摘 要 】

We consider a class of fourth order uniformly elliptic operators in planar Euclidean domains and study the associated heat kernel. For operators with L-infinity coefficients we obtain Gaussian estimates with best constants, while for operators with constant coefficients we obtain short time asymptotic estimates. The novelty of this work is that we do not assume that the associated symbol is strongly convex. The short time asymptotics reveal a behavior which is qualitatively different from that of the strongly convex case. (C) 2018 Published by Elsevier Inc.

【 授权许可】

Free