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arXiv · 1404.0288

On Liouville-type theorems and the uniqueness of the positive Cauchy problem for a class of hypoelliptic operators

Alessia E. Kogoj·Y. Pinchover·S. Polidoro
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Abstract

This note contains a representation formula for positive solutions of linear degenerate second-order equations of the form $$ \partial_t u (x,t) = \sum_{j=1}^m X_j^2 u(x,t) + X_0 u(x,t) \qquad (x,t) \in \mathbb{R}^N \times\, ]- \infty ,T[,$$ proved by a functional analytic approach based on Choquet theory. As a consequence, we obtain Liouville-type theorems and uniqueness results for the positive Cauchy problem.

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Alessia E. Kogoj, Y. Pinchover, S. Polidoro. 2014-04-01. On Liouville-type theorems and the uniqueness of the positive Cauchy problem for a class of hypoelliptic operators. https://arxiv.org/abs/1404.0288

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