Injectivity in second-gradient nonlinear elasticity
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10511031" target="_blank" >RIV/00216208:11320/25:10511031 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=mo_3iYHB.J" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=mo_3iYHB.J</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00526-025-03086-3" target="_blank" >10.1007/s00526-025-03086-3</a>
Alternative languages
Result language
angličtina
Original language name
Injectivity in second-gradient nonlinear elasticity
Original language description
We study injectivity for models of Nonlinear Elasticity that involve the second gradient. We assume that documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Omega subset {mathbb{R}}<^>n$$end{document} is a domain, documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$fin W<^>{2,q}(Omega ,{mathbb{R}}<^>n)$$end{document} satisfies documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$|J_f|<^>{-a}in L<^>1$$end{document} and that f equals a given homeomorphism on documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$partial Omega$$end{document}. Under suitable conditions on q and a we show that f must be a homeomorphism. As a main new tool we find an optimal condition for a and q that imply that documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathcal {H}<^>{n-1}({J_f=0})=0$$end{document} and hence documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$J_f$$end{document} cannot change sign. We further specify in dependence of q and a the maximal Hausdorff dimension d of the critical set documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${J_f=0}$$end{document}. The sharpness of our conditions for d is demonstrated by constructing respective counterexamples.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Calculus of Variations and Partial Differential Equations
ISSN
0944-2669
e-ISSN
1432-0835
Volume of the periodical
64
Issue of the periodical within the volume
8
Country of publishing house
US - UNITED STATES
Number of pages
29
Pages from-to
256
UT code for WoS article
001572380100003
EID of the result in the Scopus database
2-s2.0-105016612526