Departamento de Matemáticas UAM

The motivation of the problem comes from a problem of visual perception. Indeed the visual cortex has been modelled as a Lie group, with a totally degenerate metric, also called subriemannian. The associated PDE can be expressed as a sum of squares of vector fields, and the study of these type of equations under suitable geometric condition, has been started by Hormander and Rothschild – Stein. However regularity at the boundary, well known in the Euclidean setting, was still open even for the subriemannian Laplacian. We will face the problem with a suitable extension of a result of Caffarelli and Silvestre to this degenerate setting.