The paper contains a representation formula for positive solutions of linear degenerate second-order equations of the form of "sum of squares of vector fields plus a drift term" where the vector fields X_j's satisfy the Hörmander condition. It is assumed that X_j's are invariant under left translations of a Lie group and the corresponding paths satisfy a local admissibility criterion. The representation formula is established by an analytic approach based on Choquet theory. As a consequence we obtain Liouville-type theorems and uniqueness results for the positive Cauchy problem.

On Liouville-type theorems and the uniqueness of the positive Cauchy problem for a class of hypoelliptic operators / Kogoj, Alessia E.; Pinchover, Yehuda; Polidoro, Sergio. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - ELETTRONICO. - 16:4(2016), pp. 905-943. [10.1007/s00028-016-0325-7]

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

POLIDORO, Sergio
2016

Abstract

The paper contains a representation formula for positive solutions of linear degenerate second-order equations of the form of "sum of squares of vector fields plus a drift term" where the vector fields X_j's satisfy the Hörmander condition. It is assumed that X_j's are invariant under left translations of a Lie group and the corresponding paths satisfy a local admissibility criterion. The representation formula is established by an analytic approach based on Choquet theory. As a consequence we obtain Liouville-type theorems and uniqueness results for the positive Cauchy problem.
2016
16
4
905
943
On Liouville-type theorems and the uniqueness of the positive Cauchy problem for a class of hypoelliptic operators / Kogoj, Alessia E.; Pinchover, Yehuda; Polidoro, Sergio. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - ELETTRONICO. - 16:4(2016), pp. 905-943. [10.1007/s00028-016-0325-7]
Kogoj, Alessia E.; Pinchover, Yehuda; Polidoro, Sergio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1107542
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