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Propagation of low regularity for solutions of nonlinear PDEs on a riemannian manifold with a sub-Laplacian structure. (English) Zbl 06295447
Summary: Following F. Bernicot [Trans. Am. Math. Soc. 364, No. 11, 6071–6108 (2012; Zbl 1281.46028)], 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.

35S05 Pseudodifferential operators as generalizations of partial differential operators
58J47 Propagation of singularities; initial value problems on manifolds
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