Propagation of low regularity for solutions of nonlinear PDEs on a Riemannian manifold with a sub-Laplacian structure

Bernicot, Frédéric; Sire, Yannick

Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 5, pp. 935-958.

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.

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