Electron. J. Differential Equations, Vol. 2022 (2022), No. 76, pp. 111.
Heat kernel estimates for fourthorder nonuniformly elliptic operators with
nonstrongly convex symbols
Gerassimos Barbatis, Panagiotis Branikas
Abstract:
We obtain heatkernel estimates for fourthorder nonuniformly 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 Finslertype 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.
Submitted November 4, 2021. Published November 18, 2022.
Math Subject Classifications: 35K40, 47D06, 35K65, 35K67.
Key Words: Heat kernel estimates; higher order operators; singulardegenerate coefficients.
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Gerassimos Barbatis
Department of Mathematics
National and Kapodistrian University of Athens
Panepistimioupolis, 15784 Athens, Greece
email: gbarbatis@math.uoa.gr


Panagiotis Branikas
Department of Mathematics
National and Kapodistrian University of Athens
Panepistimioupolis, 15784 Athens, Greece
email: pbranikas@math.uoa.gr

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