Lifting in fractional Sobolev spaces and in VMO

Haïm Brezis; Petru Mironescu

doi:10.1007/978-1-0716-1512-6_5

Lifting in fractional Sobolev spaces and in VMO

Haïm Brezis, Petru Mironescu

School of Arts and Sciences, Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

This chapter is a follow-up to Chapter 1. We consider again maps u: Ω→ S¹, with Ω⊂ R^N, N≥ 1, smooth bounded simply connected, and our goal is to find a lifting φ “as smooth as u permits.” The difference with Chapter 1 is that u belongs either to a fractional Sobolev space W^s ^, ^p (whose definition is recalled in Section 5.1), or to the space VMO (functions of vanishing mean oscillation, whose definition is recalled in Section 5.2.1 below).

Original language	English (US)
Title of host publication	Progress in Nonlinear Differential Equations and Their Application
Publisher	Birkhauser
Pages	205-226
Number of pages	22
DOIs	https://doi.org/10.1007/978-1-0716-1512-6_5
State	Published - 2021

Publication series

Name	Progress in Nonlinear Differential Equations and Their Application
Volume	96
ISSN (Print)	1421-1750
ISSN (Electronic)	2374-0280

All Science Journal Classification (ASJC) codes

Analysis
Computational Mechanics
Mathematical Physics
Control and Optimization
Applied Mathematics

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10.1007/978-1-0716-1512-6_5

Cite this

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title = "Lifting in fractional Sobolev spaces and in VMO",

abstract = "This chapter is a follow-up to Chapter 1. We consider again maps u: Ω→ S1, with Ω⊂ RN, N≥ 1, smooth bounded simply connected, and our goal is to find a lifting φ “as smooth as u permits.” The difference with Chapter 1 is that u belongs either to a fractional Sobolev space Ws , p (whose definition is recalled in Section 5.1), or to the space VMO (functions of vanishing mean oscillation, whose definition is recalled in Section 5.2.1 below).",

author = "Ha{\"i}m Brezis and Petru Mironescu",

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AB - This chapter is a follow-up to Chapter 1. We consider again maps u: Ω→ S1, with Ω⊂ RN, N≥ 1, smooth bounded simply connected, and our goal is to find a lifting φ “as smooth as u permits.” The difference with Chapter 1 is that u belongs either to a fractional Sobolev space Ws , p (whose definition is recalled in Section 5.1), or to the space VMO (functions of vanishing mean oscillation, whose definition is recalled in Section 5.2.1 below).

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ER -

Lifting in fractional Sobolev spaces and in VMO

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