Density

Haïm Brezis; Petru Mironescu

doi:10.1007/978-1-0716-1512-6_10

Density

Haïm Brezis, Petru Mironescu

School of Arts and Sciences, Mathematics

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

Abstract

We investigate here density questions. For real-valued Sobolev spaces, C^∞(Ω¯ ; R) is dense in W^s ^, ^p(Ω; R), for any s> 0 and 1 ≤ p< ∞. This need not be true for the Sobolev spaces W^s ^, ^p(Ω; N), where N is a manifold. In particular, this is not always the case when N= S¹. We present the optimal conditions on s and p so that C^∞(Ω¯ ; S¹) is dense in W^s ^, ^p(Ω; S¹).

Original language	English (US)
Title of host publication	Progress in Nonlinear Differential Equations and Their Application
Publisher	Birkhauser
Pages	311-329
Number of pages	19
DOIs	https://doi.org/10.1007/978-1-0716-1512-6_10
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_10

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abstract = "We investigate here density questions. For real-valued Sobolev spaces, C∞(Ω¯ ; R) is dense in Ws , p(Ω; R), for any s> 0 and 1 ≤ p< ∞. This need not be true for the Sobolev spaces Ws , p(Ω; N), where N is a manifold. In particular, this is not always the case when N= S1. We present the optimal conditions on s and p so that C∞(Ω¯ ; S1) is dense in Ws , p(Ω; S1).",

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AU - Brezis, Haïm

AU - Mironescu, Petru

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AB - We investigate here density questions. For real-valued Sobolev spaces, C∞(Ω¯ ; R) is dense in Ws , p(Ω; R), for any s> 0 and 1 ≤ p< ∞. This need not be true for the Sobolev spaces Ws , p(Ω; N), where N is a manifold. In particular, this is not always the case when N= S1. We present the optimal conditions on s and p so that C∞(Ω¯ ; S1) is dense in Ws , p(Ω; S1).

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T3 - Progress in Nonlinear Differential Equations and Their Application

SP - 311

EP - 329

BT - Progress in Nonlinear Differential Equations and Their Application

PB - Birkhauser

ER -

Density

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