Sharp conditions for korn inequalities in orlicz spaces

Dominic Breit; Lars Diening

doi:10.1007/s00021-011-0082-x

Sharp conditions for korn inequalities in orlicz spaces

Dominic Breit^*, Lars Diening

^*Corresponding author for this work

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

36 Citations (Scopus)

Abstract

We show that Korn's inequality in Orlicz spaces holds if and only if the Orlicz function satisfies the Delta(2)- and the -condition. This result applies to several types of Korn's inequality. In particular we show that Korn's inequality is false in L (1), in L log L, in Exp and in L (a).

Original language	English
Pages (from-to)	565-573
Number of pages	9
Journal	Journal of Mathematical Fluid Mechanics
Volume	14
Issue number	3
DOIs	https://doi.org/10.1007/s00021-011-0082-x
Publication status	Published - Sept 2012

Keywords

Korn's inequality in L log L
Korn's inequality in Orlicz spaces
Counter example
Prandtl-Eyring fluids
REGULARITY
COUNTEREXAMPLES
OPERATORS
DOMAINS

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10.1007/s00021-011-0082-x

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abstract = "We show that Korn's inequality in Orlicz spaces holds if and only if the Orlicz function satisfies the Delta(2)- and the -condition. This result applies to several types of Korn's inequality. In particular we show that Korn's inequality is false in L (1), in L log L, in Exp and in L (a).",

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AU - Diening, Lars

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AB - We show that Korn's inequality in Orlicz spaces holds if and only if the Orlicz function satisfies the Delta(2)- and the -condition. This result applies to several types of Korn's inequality. In particular we show that Korn's inequality is false in L (1), in L log L, in Exp and in L (a).

KW - Korn's inequality in L log L

KW - Korn's inequality in Orlicz spaces

KW - Counter example

KW - Prandtl-Eyring fluids

KW - REGULARITY

KW - COUNTEREXAMPLES

KW - OPERATORS

KW - DOMAINS

UR - https://www.scopus.com/pages/publications/84862986910

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DO - 10.1007/s00021-011-0082-x

M3 - Article

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VL - 14

SP - 565

EP - 573

JO - Journal of Mathematical Fluid Mechanics

JF - Journal of Mathematical Fluid Mechanics

IS - 3

ER -

Sharp conditions for korn inequalities in orlicz spaces

Abstract

Keywords

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