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

2020/12/07 by Gerassimos Barbatis, Barbatis, Gerassimos, Panagiotis Branikas +1
Computer Science · Mathematics · #35K40 47D06 (primary) 35K65 35K67 (secondary) #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2012.03615

openalex publication_date 2020/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain heat kernel estimates for a class of fourth order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols that are not strongly convex. This rises 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 inequalitry and an interpolation inequality, which are related to the singularity or degeneracy of the coefficients.

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