Schauder estimates at the boundary in Carnot groups

Geometric Aspects of Nonlinear Partial Differential Equations

22 November 14:00 - 15:00

Giovanna Citti - University of Bologna

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. 
Panagiota Daskalopoulos
Columbia University
Alessio Figalli
ETH Zürich
Erik Lindgren
Uppsala University
Henrik Shahgholian
KTH Royal Institute of Technology
Susanna Terracini,
University of Turin


Erik Lindgren

Henrik Shahgholian


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