JournalsaihpcVol. 30, No. 5pp. 935–958

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

  • Frédéric Bernicot

    CNRS, Université de Nantes, Laboratoire Jean Leray, 2, rue de la Houssinière, 44322 Nantes cedex 3, France

  • Yannick Sire

    LATP-UMR7353-Université Aix-Marseille, 13397 Marseille, France
Propagation of low regularity for solutions of nonlinear PDEs on a Riemannian manifold with a sub-Laplacian structure cover
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Abstract

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.

Cite this article

Frédéric Bernicot, Yannick Sire, Propagation of low regularity for solutions of nonlinear PDEs on a Riemannian manifold with a sub-Laplacian structure. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 5, pp. 935–958

DOI 10.1016/J.ANIHPC.2012.12.005