Trace-Free Korn Inequalities in Orlicz Spaces

Dominic Breit; Andrea Cianchi; Lars Diening

doi:10.1137/16M1073662

Trace-Free Korn Inequalities in Orlicz Spaces

Dominic Breit^*, Andrea Cianchi, Lars Diening

^*Corresponding author for this work

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

23 Citations (Scopus)

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Abstract

Necessary and suffcient conditions are exhibited for a Korn-type inequality to hold between (possibly different) Orlicz norms of the gradient of vector-valued functions and of the deviatoric part of their symmetric gradients. As a byproduct of our approach, a positive answer is given to the question of the necessity of the same sufficient conditions in related Korn-type inequalities for the full symmetric gradient, for negative Orlicz-Sobolev norms, and for the gradient of the Bogovskii operator.

Original language	English
Pages (from-to)	2496-2526
Number of pages	31
Journal	SIAM Journal on Mathematical Analysis
Volume	49
Issue number	4
DOIs	https://doi.org/10.1137/16M1073662
Publication status	Published - 6 Jul 2017

Keywords

Korn inequality
Orlicz spaces
Singular integrals
Symmetric gradient
Trace-free symmetric gradient

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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AU - Cianchi, Andrea

AU - Diening, Lars

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AB - Necessary and suffcient conditions are exhibited for a Korn-type inequality to hold between (possibly different) Orlicz norms of the gradient of vector-valued functions and of the deviatoric part of their symmetric gradients. As a byproduct of our approach, a positive answer is given to the question of the necessity of the same sufficient conditions in related Korn-type inequalities for the full symmetric gradient, for negative Orlicz-Sobolev norms, and for the gradient of the Bogovskii operator.

KW - Korn inequality

KW - Orlicz spaces

KW - Singular integrals

KW - Symmetric gradient

KW - Trace-free symmetric gradient

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JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 4

ER -

Trace-Free Korn Inequalities in Orlicz Spaces

Abstract

Keywords

ASJC Scopus subject areas

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