An extension of Hörmander's theorem for infinitely degenerate second-order operators
type: Item
instance of: scholarly article
title: An extension of Hörmander's theorem for infinitely degenerate second-order operators
zbMATH Open document ID: 0840.60053
DOI: 10.1215/S0012-7094-95-07822-3
author: Salah Mohammed
author: Denis R. Bell
published in: Duke Mathematical Journal
publication date: 1996-06-18T00:00:00Z
review text: The hypoellipticity of a class of second-order operators \(L\) which do not satisfy Hörmander's conditions is proved. More precisely, it is assumed that the set of points where these conditions do not hold is contained in a submanifold of codimension 1; then the result is proved under another assumption concerning the behaviour near this submanifold. The parabolic equation associated to the operator \(L + \partial/ \partial t\) is also studied. The proofs of these results are probabilistic, and are based on Itô's and Malliavin's calculus.
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35K10
zbMATH DE Number: 815773
zbMATH Keywords: Hörmander's theorem
zbMATH Keywords: hypoellipticity of degenerate operators
reviewed by: Jean Picard
MaRDI profile type: Publication
cites work: Q3834799
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full work available at URL: s0012-7094-95-07822-3
OpenAlex ID: W1529641647
description: scientific article; zbMATH DE number 815773