Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces

Haïm Brezis (1) , Petru Mironescu (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 EDPA

Our main result is that, when $f$ is smooth and has bounded derivatives, and when $u$ belongs to the spaces $W^{s,p}$ and $W^{1,sp}$, the map $f(u)$ is in $W^{s,p}$.

Mots clés: composition; Sobolev spaces; paraproducts

Domaines: Analyse classique [math.CA]

Haïm Brezis, Petru Mironescu. Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces. Journal of Evolution Equations, 2001, 1 (4), pp.387-404. ⟨10.1007/PL00001378⟩. ⟨hal-00747694⟩