Lifting in Sobolev spaces

Jean Bourgain (1) , Haïm Brezis (2) , Petru Mironescu (3)

1 IAS - Institute for Advanced Study
2 LJLL - Laboratoire Jacques-Louis Lions
3 EDPA

We characterize the couples $(s,p)$ with the following property: if $u$ is a complex-valued unimodular map in $W^{s,p}$, then $u$ has (locally) a phase in $W^{s,p}$.

Mots clés: lifting; unimodular maps; Sobolev spaces

Domaines: Analyse classique [math.CA]

Jean Bourgain, Haïm Brezis, Petru Mironescu. Lifting in Sobolev spaces. Journal d'analyse mathématique, 2000, 80, pp.37-86. ⟨10.1007/BF02791533⟩. ⟨hal-00747691⟩