Hôlder continuity for quasilinear hypoelliptic equations

C Imbert (1) , Clément Mouhot (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We prove that L2 weak solutions to a quasilinear hypoellip-tic equations with bounded measurable coefficients are Hölder continuous. The proof relies on classical techniques developed by De Giorgi and Moser together with the averaging lemma developed in kinetic theory. The latter tool is used in the proof of the local gain of integrability of sub-solutions and in the proof of an " hypoelliptic isoperimetric De Giorgi lemma " , obtained by combining the classical isoperimetric inequality on the diffusive variable with the structure of the integral curves of the first-order part of the operator.

Mots clés: De Giorgi method; Hölder continuity; averaging lemma; Hypoelliptic equations; Moser iteration

Domaines: Equations aux dérivées partielles [math.AP]

C Imbert, Clément Mouhot. Hôlder continuity for quasilinear hypoelliptic equations. 2015. ⟨hal-01152145v2⟩