Rendiconti Lincei - Matematica e Applicazioni

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Volume 18, Issue 4, 2007, pp. 333–342
DOI: 10.4171/RLM/499

Gaussian estimates for hypoelliptic operators via optimal control

Ugo Boscain[1] and Sergio Polidoro[2]

(1) Dipartimento di Matematica, SISSA, Via Beirut, 2-4, 34014, TRIESTE, ITALY
(2) Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato, 5, 40127, BOLOGNA, ITALY

We obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality. Our main result is given in terms of the value function of a suitable optimal control problem.

Keywords: Hypoelliptic equations, Lie groups, Gaussian bounds, optimal control theory

Boscain U, Polidoro S. Gaussian estimates for hypoelliptic operators via optimal control. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), 333-342. doi: 10.4171/RLM/499