HOLDER CONTINUITY OF SOLUTIONS TO QUASILINEAR HYPOELLIPTIC EQUATIONS

Cyril Imbert (1) , Clément Mouhot (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 CAM - University of Cambridge [UK]

We prove that L2 weak solutions to a quasilinear hypoelliptic equations with rough coefficients are Hölder continuous. The proof relies on classical techniques developed by De Giorgi and Moser together with the averaging lemma developped 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.

Domaines: Equations aux dérivées partielles [math.AP]

Cyril Imbert, Clément Mouhot. HOLDER CONTINUITY OF SOLUTIONS TO QUASILINEAR HYPOELLIPTIC EQUATIONS. 2015. ⟨hal-01152145v1⟩