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math.AP2022
A trajectorial interpretation of Moser's proof of the Harnack inequality
Lukas Niebel, Rico Zacher
In 1971 Moser published a simplified version of his proof of the parabolic Harnack inequality. The core new ingredient is a fundamental lemma due to Bombieri and Giusti, which comb…
math.AP2022
On a kinetic Poincaré inequality and beyond
Lukas Niebel, Rico Zacher
In this article, we give a trajectorial proof of a kinetic Poincaré inequality which plays an important role in the De Giorgi-Nash-Moser theory for kinetic equations. The present w…