Propagation of low regularity for solutions of nonlinear PDEs on a Riemannian manifold with a sub-Laplacian structure
Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 5, p. 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.
DOI : https://doi.org/10.1016/j.anihpc.2012.12.005
Classification:  35S05,  58J47
Keywords: Paralinearization, Sub-Laplacian operator, Riemannian manifold
@article{AIHPC_2013__30_5_935_0,
     author = {Bernicot, Fr\'ed\'eric and Sire, Yannick},
     title = {Propagation of low regularity for solutions of nonlinear PDEs on a Riemannian manifold with a sub-Laplacian structure},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {30},
     number = {5},
     year = {2013},
     pages = {935-958},
     doi = {10.1016/j.anihpc.2012.12.005},
     zbl = {06295447},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2013__30_5_935_0}
}
Bernicot, Frédéric; Sire, Yannick. Propagation of low regularity for solutions of nonlinear PDEs on a Riemannian manifold with a sub-Laplacian structure. Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 5, pp. 935-958. doi : 10.1016/j.anihpc.2012.12.005. http://www.numdam.org/item/AIHPC_2013__30_5_935_0/

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