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) CMAP - Centre de Mathématiques Appliquées, Ecole Polytechnique, Route de Saclay, 91128, PALAISEAU CEDEX, FRANCE
(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 Ugo, Polidoro Sergio: 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