Sobolev inequalities with symmetry

Yonggeun Cho; Tohru Ozawa

doi:10.1142/S0219199709003399

Sobolev inequalities with symmetry

Yonggeun Cho^*
, Tohru Ozawa

^*Corresponding author for this work

Department of Mathematics

Waseda University

Research output: Contribution to journal › Journal article › peer-review

102 Scopus citations

Abstract

In this paper, we derive some Sobolev inequalities for radially symmetric functions in ^s with 1/2 < s < n/2. We show the end point case s = 1/2 on the homogeneous Besov space B_2,1^1/2. These results are extensions of the well-known Strauss' inequality [13]. Also non-radial extensions are given, which show that compact embeddings are possible in some L^p spaces if a suitable angular regularity is imposed.

Original language	English
Pages (from-to)	355-365
Number of pages	11
Journal	Communications in Contemporary Mathematics
Volume	11
Issue number	3
DOIs	https://doi.org/10.1142/S0219199709003399
State	Published - 2009.06

Keywords

Angular regularity.
Function space with radial symmetry
Sobolev inequality

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1142/S0219199709003399

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@article{57c41e3813a24ef89a45a6afb46afddd,

title = "Sobolev inequalities with symmetry",

abstract = "In this paper, we derive some Sobolev inequalities for radially symmetric functions in s with 1/2 < s < n/2. We show the end point case s = 1/2 on the homogeneous Besov space B2,11/2. These results are extensions of the well-known Strauss' inequality [13]. Also non-radial extensions are given, which show that compact embeddings are possible in some Lp spaces if a suitable angular regularity is imposed.",

keywords = "Angular regularity., Function space with radial symmetry, Sobolev inequality",

author = "Yonggeun Cho and Tohru Ozawa",

year = "2009",

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language = "English",

volume = "11",

pages = "355--365",

journal = "Communications in Contemporary Mathematics",

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T1 - Sobolev inequalities with symmetry

AU - Cho, Yonggeun

AU - Ozawa, Tohru

PY - 2009/6

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N2 - In this paper, we derive some Sobolev inequalities for radially symmetric functions in s with 1/2 < s < n/2. We show the end point case s = 1/2 on the homogeneous Besov space B2,11/2. These results are extensions of the well-known Strauss' inequality [13]. Also non-radial extensions are given, which show that compact embeddings are possible in some Lp spaces if a suitable angular regularity is imposed.

AB - In this paper, we derive some Sobolev inequalities for radially symmetric functions in s with 1/2 < s < n/2. We show the end point case s = 1/2 on the homogeneous Besov space B2,11/2. These results are extensions of the well-known Strauss' inequality [13]. Also non-radial extensions are given, which show that compact embeddings are possible in some Lp spaces if a suitable angular regularity is imposed.

KW - Angular regularity.

KW - Function space with radial symmetry

KW - Sobolev inequality

UR - https://www.scopus.com/pages/publications/68049124964

U2 - 10.1142/S0219199709003399

DO - 10.1142/S0219199709003399

M3 - Journal article

AN - SCOPUS:68049124964

SN - 0219-1997

VL - 11

SP - 355

EP - 365

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

IS - 3

ER -

Sobolev inequalities with symmetry

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

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