Hypoelliptic estimates for linear transport operators

Paul Alphonse (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We aim at understanding how the non-commutation phenomena between a linear transport operator and a fractional diffusion allow the transport operator to satisfy hypoelliptic estimates on the whole space. Such hypoelliptic estimates are obtained for a large class of linear transport operators by using the classical multiplier method. The main motivation of this work arises from the study of the hypoelliptic regularity of the solutions of kinetic equations associated with a free transport operator.

Mots clés: linear transport operators; hypoelliptic estimates; Kalman rank condition; multiplier method

Domaines: Equations aux dérivées partielles [math.AP]

Paul Alphonse. Hypoelliptic estimates for linear transport operators. 2020. ⟨hal-02896921⟩