Heat kernel estimates for fourth-order non-uniformly elliptic operators with non-strongly convex symbols

Electronic Journal of Differential Equations

article

Gerassimos Barbatis¹  Panagiotis Branikas¹ 

[1] Department of Mathematics National and Kapodistrian University of Athens Panepistimioupolis

关键词: Heat kernel estimates;    higher order operators;    singular-degenerate coefficients.;   

DOI  :  10.58997/ejde.2022.76

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

We obtain heat-kernel estimates for fourth-order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols that are not strongly convex. This entails certain difficulties as it is known that, as opposed to the strongly convex case, there is no absolute exponential constant. Our estimates involve sharp constants and Finsler-type distances that are induced by the operator symbol. The main result is based on two general hypotheses, a weighted Sobolev inequality and an interpolation inequality, which are related to the singularity or degeneracy of the coefficients.

【 授权许可】

CC BY