Attainability of the best Sobolev constant in a ball

Norisuke Ioku

doi:10.1007/s00208-018-1776-7

Attainability of the best Sobolev constant in a ball

Norisuke Ioku

Research output: Contribution to journal › Article

1 Citation (Scopus)

Abstract

The best constant in the Sobolev inequality in the whole space is attained by the Aubin–Talenti function; however, this does not happen in bounded domains because of the break down of the dilation invariance. In this paper, we investigate a new scale invariant form of the Sobolev inequality in a ball and show that its best constant is attained by functions of the Aubin–Talenti type. Generalization to the Caffarelli–Kohn–Nirenberg inequality in a ball is also discussed.

Original language	English
Journal	Mathematische Annalen
Volume	375
Issue number	1-2
DOIs	https://doi.org/10.1007/s00208-018-1776-7
Publication status	Published - 2019 Oct 8
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/s00208-018-1776-7

Fingerprint Dive into the research topics of 'Attainability of the best Sobolev constant in a ball'. Together they form a unique fingerprint.

Cite this

@article{b40fde3394114110a1c2eaac858d6a5e,

title = "Attainability of the best Sobolev constant in a ball",

abstract = "The best constant in the Sobolev inequality in the whole space is attained by the Aubin–Talenti function; however, this does not happen in bounded domains because of the break down of the dilation invariance. In this paper, we investigate a new scale invariant form of the Sobolev inequality in a ball and show that its best constant is attained by functions of the Aubin–Talenti type. Generalization to the Caffarelli–Kohn–Nirenberg inequality in a ball is also discussed.",

author = "Norisuke Ioku",

year = "2019",

month = oct,

day = "8",

doi = "10.1007/s00208-018-1776-7",

language = "English",

volume = "375",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer New York",

number = "1-2",

}

TY - JOUR

T1 - Attainability of the best Sobolev constant in a ball

AU - Ioku, Norisuke

PY - 2019/10/8

Y1 - 2019/10/8

N2 - The best constant in the Sobolev inequality in the whole space is attained by the Aubin–Talenti function; however, this does not happen in bounded domains because of the break down of the dilation invariance. In this paper, we investigate a new scale invariant form of the Sobolev inequality in a ball and show that its best constant is attained by functions of the Aubin–Talenti type. Generalization to the Caffarelli–Kohn–Nirenberg inequality in a ball is also discussed.

AB - The best constant in the Sobolev inequality in the whole space is attained by the Aubin–Talenti function; however, this does not happen in bounded domains because of the break down of the dilation invariance. In this paper, we investigate a new scale invariant form of the Sobolev inequality in a ball and show that its best constant is attained by functions of the Aubin–Talenti type. Generalization to the Caffarelli–Kohn–Nirenberg inequality in a ball is also discussed.

UR - http://www.scopus.com/inward/record.url?scp=85056664135&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056664135&partnerID=8YFLogxK

U2 - 10.1007/s00208-018-1776-7

DO - 10.1007/s00208-018-1776-7

M3 - Article

AN - SCOPUS:85056664135

VL - 375

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 1-2

ER -