Hölder continuity of solutions to hypoelliptic equations with rough coefficients

Monday, October 5, 2015 -
3:15pm to 4:30pm
The celebrated De Giorgi-Nash theory about Hölder continuity of solutions to elliptic or parabolic equations with rough --i.e. merely measurable-- coefficients in the late 1950s is a cornerstone of modern PDE analysis. We extend this theory to a class of kinetic equation of Vlasov-Fokker-Planck type ("hypoelliptic of type II" in the terminology of Hörmander) where a first-order hyperbolic operator interacts with a partially elliptic operator with rough coefficients. We also extend the theory of Moser about Harnack inequalities for these equations. This is a joint work with F. Golse, C. Imbert and A. Vasseur.
Clement Mouhot
Cambridge University
Event Location: 
Fine Hall 110