Speaker: Giovanna Citti (University of Bologna)
Title: Schauder estimates at the boundary in Carnot groups
Abstract: We present a joint work with A. Baldi and G.Cupini on Schauder estimates at the boundary for sub-Laplacian type operators in Carnot groups. Up to now subriemannian estimates at the boundary are known only in the Heisenberg group, but the proof, due to Jerison, is based on the Fourier transform and cannot be repeated in general Lie groups. In this paper we introduce a new method, which allows to build a Poisson kernel starting from the fundamental solution, and to deduce the estimates.