# Mean value formulas for Ornstein-Uhlenbeck and Hermite temperatures

## TL;DR

This paper derives explicit mean value formulas for solutions to diffusion equations linked with Ornstein-Uhlenbeck and Hermite operators, leading to important properties like maximum principles and Harnack inequalities.

## Contribution

It introduces explicit mean value formulas for these diffusion equations, enabling new proofs of classical properties and inequalities.

## Key findings

- Derived explicit mean value formulas for Ornstein-Uhlenbeck and Hermite equations.
- Established maximum principles and uniqueness theorems.
- Proved Harnack-type inequalities for solutions.

## Abstract

We obtain explicit mean value formulas for the solutions of the diffusion equations associated with the Ornstein-Uhlenbeck and Hermite operators. From these, we derive various useful properties, such as maximum principles, uniqueness theorems and Harnack-type inequalities.

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Source: https://tomesphere.com/paper/1902.06102