{"title":"Lifting of fractional Sobolev mappings to noncompact covering spaces","authors":"Jean Van Schaftingen","doi":"10.4171/aihpc/98","DOIUrl":null,"url":null,"abstract":"Given compact Riemannian manifolds $\\mathcal{M}$ and $\\mathcal{N}$, a Riemannian covering $\\pi : \\smash{\\widetilde{\\mathcal{N}}} \\to \\mathcal{N}$ by a noncompact covering space $\\smash{\\widetilde{\\mathcal{N}}}$, $1<p<\\infty$ and $0<s<1$, the space of liftings of fractional Sobolev maps in $\\smash{\\dot{W}^{s, p}} (\\mathcal{M}, \\mathcal{N})$ is characterized when $sp>1$ and an optimal nonlinear fractional Sobolev estimate is obtained when moreover $sp \\ge \\dim \\mathcal{M}$. A nonlinear characterization of the sum of spaces $\\smash{\\dot{W}^{s, p}} (\\mathcal{M}, \\mathbb{R}) + \\smash{\\dot{W}^{1, sp}} (\\mathcal{M}, \\mathbb{R})$ is also provided.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/aihpc/98","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
Given compact Riemannian manifolds $\mathcal{M}$ and $\mathcal{N}$, a Riemannian covering $\pi : \smash{\widetilde{\mathcal{N}}} \to \mathcal{N}$ by a noncompact covering space $\smash{\widetilde{\mathcal{N}}}$, $1
1$ and an optimal nonlinear fractional Sobolev estimate is obtained when moreover $sp \ge \dim \mathcal{M}$. A nonlinear characterization of the sum of spaces $\smash{\dot{W}^{s, p}} (\mathcal{M}, \mathbb{R}) + \smash{\dot{W}^{1, sp}} (\mathcal{M}, \mathbb{R})$ is also provided.
期刊介绍:
The Nonlinear Analysis section of the Annales de l''Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.