Seminár PDE – Annalaura Rebucci (MPI MiS Leipzig)

Prekladám do slovenčiny…

Title: De Giorgi methods for kinetic hypoelliptic equations Abstract: We present new results that extend the De Giorgi-Nash-Moser theory to a class of hypoelliptic equations arising in kinetic theory. These operators are mathematically characterized by two parts: a diffusion part in the velocity variables governed by the (fractional) Laplace operator, and a first order differential operator which propagates smoothness in the remaining spatial variables. A key ingredient to prove our results is a Poincaré inequality adapted to the hypoelliptic geometry. This allows us to treat equations with a…