A note on strong-form stability for the Sobolev inequality

Robin Neumayer*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

In this note, we establish a strong form of the quantitive Sobolev inequality in Euclidean space for p∈ (1 , n). Given any function u∈ W˙ 1 , p(Rn) , the gap in the Sobolev inequality controls ‖ ∇ u- ∇ v‖ p, where v is an extremal function for the Sobolev inequality.

Original languageEnglish (US)
Article number25
JournalCalculus of Variations and Partial Differential Equations
Volume59
Issue number1
DOIs
StatePublished - Feb 1 2020

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Sobolev Inequality
Extremal Function
Euclidean space
Form

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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abstract = "In this note, we establish a strong form of the quantitive Sobolev inequality in Euclidean space for p∈ (1 , n). Given any function u∈ W˙ 1 , p(Rn) , the gap in the Sobolev inequality controls ‖ ∇ u- ∇ v‖ p, where v is an extremal function for the Sobolev inequality.",
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A note on strong-form stability for the Sobolev inequality. / Neumayer, Robin.

In: Calculus of Variations and Partial Differential Equations, Vol. 59, No. 1, 25, 01.02.2020.

Research output: Contribution to journalArticle

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