A proof of Hörmander's theorem for sublaplacians on Carnot groups. (October 2015)

• Record Type: Journal Article
• Authors: Bramanti, Marco; Brandolini, Luca
• Is Part Of: Nonlinear analysis. Volume 126(2015)
• Page Start: 170
• Page End: 200
• Publication Date: 2015-10
• Subjects: Hypoelliptic operators -- Hörmander's hypoellipticity theorem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.02.021
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We give a self-contained analytical proof of Hörmander'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.