Skip to main content

Giovanna Citti: Schauder estimates at the boundary in Carnot groups

Time: Tue 2022-11-08 14.00 - 15.00

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

Video link: Meeting ID: 921 756 1880

Participating: Giovanna Citti - University of Bologna

Export to calendar


We prove Schauder estimates at the boundary for sub-Laplacians in Carnot groups. While sub-Riemannian internal Schauder estimates are well known, the estimates at the boundary were known only in the Heisenberg group. Here we face the problem in general Carnot groups at non characteristic points, building a Poisson kernel in term of the fundamental solution. In collaboration with Baldi and Cupini we provide a first result, related to the Caffarelli Silvestre approach, which can be applied if the boundary is an Hörmander structure. In a second result, obtained in collaboration with Giovannardi and Sire, we remove this assumption in case of H-type groups, using a double potential method.