Propagation of low regularity for solutions of nonlinear PDEs on a Riemannian manifold with a sub-Laplacian structure
Frédéric Bernicot, Yannick Sire · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 2013
Following Bernicot (2012) [7], we introduce a notion of paraproducts associated to a semigroup. We do not use Fourier transform arguments and the background manifold is doubling, endowed with a sub-Laplacian structure. Our main result is a paralinearization theorem in a non-Euclidean framework, with an application to the propagation of regularity for some nonlinear PDEs.