Liouville heat kernel: regularity and bounds
Pascal Maillard, R\'emi Rhodes, Vincent Vargas, Ofer Zeitouni
TL;DR
This paper investigates the analytic properties of the Liouville heat kernel, establishing regularity estimates and deriving significant bounds to better understand its behavior.
Contribution
It introduces new regularity estimates and bounds for the Liouville heat kernel, advancing the mathematical understanding of its properties.
Findings
Established regularity estimates for the Liouville heat kernel
Derived non-trivial lower bounds
Derived non-trivial upper bounds
Abstract
We initiate in this paper the study of analytic properties of the Liouville heat kernel. In particular, we establish regularity estimates on the heat kernel and derive non trivial lower and upper bounds.
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Taxonomy
TopicsNumerical methods in inverse problems · Spectral Theory in Mathematical Physics · Advanced Thermodynamics and Statistical Mechanics