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SIAM Journal on Mathematical Analysis
Article
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arXiv.org e-Print Archive
Preprint . 2008
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SIAM Journal on Mathematical Analysis
Article . 2010 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2008
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Article . 2010
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https://dx.doi.org/10.1137/080...
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https://dx.doi.org/10.1137/080...
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Multiwell Rigidity in Nonlinear Elasticity

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2010Embargo end date: 01 Feb 2008 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Mathematical Analysis, volume 42, pages 1,986-2,012 (issn: 0036-1410, eissn: 1095-7154, Copyright policy )
Authors: Milena Chermisi; Sergio Conti;

doi: 10.1137/080714968 , 10.48550/arxiv.0802.0955

arXiv: 0802.0955

Multiwell Rigidity in Nonlinear Elasticity

Abstract

We derive a quantitative rigidity estimate for a multiwell problem in nonlinear elasticity. Precisely, we show that if a gradient field is L^1-close to a set of the form SO(n)U_1 \cup ... \cup SO(n)U_l, and an appropriate bound on the length of the interfaces holds, then the gradient field is actually close to only one of the wells SO(n)U_i. The estimate holds for any connected subdomain, and has the optimal scaling.

23 pages, 3 figures

Keywords

Mathematics - Analysis of PDEs, 53C24 (Primary) 74B20 (Secondary), FOS: Mathematics, Analysis of PDEs (math.AP)

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    popularity
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    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
12
Top 10%
Average
Average
Green
bronze