We give a self-contained analytical proof of H ̈ormander’s hypoellipticity theorem in the case of left invariant sub-laplacians of Carnot groups. The proof does not rely on pseudodifferential calculus and provides intermediate regularity estimates expressed in terms of Sobolev spaces induced by right invariant vector fields.
A proof of Hörmander’s theorem for sublaplacians on Carnot groups
Bramanti, Marco;
2015-01-01
Abstract
We give a self-contained analytical proof of H ̈ormander’s hypoellipticity theorem in the case of left invariant sub-laplacians of Carnot groups. The proof does not rely on pseudodifferential calculus and provides intermediate regularity estimates expressed in terms of Sobolev spaces induced by right invariant vector fields.File in questo prodotto:
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