On the proof of Hörmander's hypoellipticity theorem
This is a survey paper about the proof of the hypoellipticity theorem by Hörmander (Acta Math. 1967). We will compare three different proofs of this result: the original one by Hörmander, the proof given by Kohn (Proc. Sympos. Pure Math., 1973) and independently by Oleĭnik and Radkevič in their 1973 monograph, and the more recent proof of a special case of this result, concerning sublaplacians on Carnot groups, given by Bramanti and Brandolini (Nonlinear Analysis, 2015).
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