Gradient stability for the Sobolev inequality: The case p ≥ 2

Alessio Figalli; Robin Neumayer

doi:10.4171/JEMS/837

Gradient stability for the Sobolev inequality: The case p ≥ 2

Alessio Figalli, Robin Neumayer

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We prove a strong form of the quantitative Sobolev inequality in Rⁿ for p ≥ 2, where the deficit of a function u ∈ W ^1,p controls k∇u−∇vk_Lp for an extremal function v in the Sobolev inequality.

Original language	English (US)
Pages (from-to)	319-354
Number of pages	36
Journal	Journal of the European Mathematical Society
Volume	21
Issue number	2
DOIs	https://doi.org/10.4171/JEMS/837
State	Published - 2019

Keywords

Quantitative inequalities
Sobolev inequality
Stability

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.4171/JEMS/837

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title = "Gradient stability for the Sobolev inequality: The case p ≥ 2",

abstract = "We prove a strong form of the quantitative Sobolev inequality in Rn for p ≥ 2, where the deficit of a function u ∈ W 1,p controls k∇u−∇vkLp for an extremal function v in the Sobolev inequality.",

keywords = "Quantitative inequalities, Sobolev inequality, Stability",

author = "Alessio Figalli and Robin Neumayer",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society 2019",

year = "2019",

doi = "10.4171/JEMS/837",

language = "English (US)",

volume = "21",

pages = "319--354",

journal = "Journal of the European Mathematical Society",

issn = "1435-9855",

publisher = "European Mathematical Society Publishing House",

number = "2",

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TY - JOUR

T1 - Gradient stability for the Sobolev inequality

T2 - The case p ≥ 2

AU - Figalli, Alessio

AU - Neumayer, Robin

N1 - Publisher Copyright: © European Mathematical Society 2019

PY - 2019

Y1 - 2019

N2 - We prove a strong form of the quantitative Sobolev inequality in Rn for p ≥ 2, where the deficit of a function u ∈ W 1,p controls k∇u−∇vkLp for an extremal function v in the Sobolev inequality.

AB - We prove a strong form of the quantitative Sobolev inequality in Rn for p ≥ 2, where the deficit of a function u ∈ W 1,p controls k∇u−∇vkLp for an extremal function v in the Sobolev inequality.

KW - Quantitative inequalities

KW - Sobolev inequality

KW - Stability

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U2 - 10.4171/JEMS/837

DO - 10.4171/JEMS/837

M3 - Article

AN - SCOPUS:85060853085

SN - 1435-9855

VL - 21

SP - 319

EP - 354

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 2

ER -

Gradient stability for the Sobolev inequality: The case p ≥ 2

Abstract

Keywords

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