Article Dans Une Revue Nonlinear Analysis: Theory, Methods and Applications Année : 2020

Lifting in Besov spaces

Résumé

Let $\Omega$ be a smooth bounded domain in ${\mathbb R}^n$ and $u$ be a measurable function on $\Omega$ such that $|u(x)|=1$ almost everywhere in $\Omega$. Assume that $u$ belongs to the $B^s_{p,q}(\Omega)$ Besov space. We investigate whether there exists a real-valued function $\varphi\in B^s_{p,q}$ such that $u=e^{i\varphi}$. This extends the corresponding study in Sobolev spaces due to Bourgain, Brezis and the first author. The analysis of this lifting problem leads us to prove some interesting new properties of Besov spaces, in particular a non restriction property when $q>p$.

Fichier principal
Vignette du fichier
lifting_besov_20190305.pdf (354.21 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence
Loading...

Dates et versions

hal-01517735 , version 1 (03-05-2017)
hal-01517735 , version 2 (22-06-2017)
hal-01517735 , version 3 (08-03-2019)

Licence

Identifiants

Citer

Petru Mironescu, Emmanuel Russ, Yannick Sire. Lifting in Besov spaces. Nonlinear Analysis: Theory, Methods and Applications, 2020, Nonlocal and fractional phenomena, 193, ⟨10.1016/j.na.2019.03.012⟩. ⟨hal-01517735v3⟩
1098 Consultations
1179 Téléchargements

Altmetric

Partager

  • More