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New relaxation theorems with applications to strong materials. / Mandallena, Jean Philippe; Sychev, Mikhail.

In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 148, No. 5, 01.10.2018, p. 1029-1047.

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Harvard

Mandallena, JP & Sychev, M 2018, 'New relaxation theorems with applications to strong materials', Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol. 148, no. 5, pp. 1029-1047. https://doi.org/10.1017/S0308210518000082

APA

Mandallena, J. P., & Sychev, M. (2018). New relaxation theorems with applications to strong materials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 148(5), 1029-1047. https://doi.org/10.1017/S0308210518000082

Vancouver

Mandallena JP, Sychev M. New relaxation theorems with applications to strong materials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2018 Oct 1;148(5):1029-1047. doi: 10.1017/S0308210518000082

Author

Mandallena, Jean Philippe ; Sychev, Mikhail. / New relaxation theorems with applications to strong materials. In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2018 ; Vol. 148, No. 5. pp. 1029-1047.

BibTeX

@article{0d33c4fb552849d385c8593aa536cb4f,
title = "New relaxation theorems with applications to strong materials",
abstract = "Recently, Sychev showed that conditions both necessary and sufficient for lower semicontinuity of integral functionals with p-coercive extended-valued integrands are the W1,p-quasi-convexity and the validity of a so-called matching condition (M). Condition (M) is so general that we conjecture whether it always holds in the case of continuous integrands. In this paper we develop the relaxation theory under the validity of condition (M). It turns out that a better relaxation theory is available in this case. This motivates our research since it is an important old open problem to develop the relaxation theory in the case of extended-value integrands. Then we discuss applications of the general relaxation theory to some concrete cases, in particular to the theory of strong materials.",
keywords = "extended-valued integrand, lower semicontinuity, relaxation, strong materials, W-quasi-convexity, ENERGY, MINIMA, CALCULUS, GRADIENT, NONLINEAR ELASTICITY, INTEGRALS, GROWTH, W-1;p-quasi-convexity, LOWER SEMICONTINUITY, CONVERGENCE",
author = "Mandallena, {Jean Philippe} and Mikhail Sychev",
year = "2018",
month = oct,
day = "1",
doi = "10.1017/S0308210518000082",
language = "English",
volume = "148",
pages = "1029--1047",
journal = "Proceedings of the Royal Society of Edinburgh Section A: Mathematics",
issn = "0308-2105",
publisher = "Cambridge University Press",
number = "5",

}

RIS

TY - JOUR

T1 - New relaxation theorems with applications to strong materials

AU - Mandallena, Jean Philippe

AU - Sychev, Mikhail

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Recently, Sychev showed that conditions both necessary and sufficient for lower semicontinuity of integral functionals with p-coercive extended-valued integrands are the W1,p-quasi-convexity and the validity of a so-called matching condition (M). Condition (M) is so general that we conjecture whether it always holds in the case of continuous integrands. In this paper we develop the relaxation theory under the validity of condition (M). It turns out that a better relaxation theory is available in this case. This motivates our research since it is an important old open problem to develop the relaxation theory in the case of extended-value integrands. Then we discuss applications of the general relaxation theory to some concrete cases, in particular to the theory of strong materials.

AB - Recently, Sychev showed that conditions both necessary and sufficient for lower semicontinuity of integral functionals with p-coercive extended-valued integrands are the W1,p-quasi-convexity and the validity of a so-called matching condition (M). Condition (M) is so general that we conjecture whether it always holds in the case of continuous integrands. In this paper we develop the relaxation theory under the validity of condition (M). It turns out that a better relaxation theory is available in this case. This motivates our research since it is an important old open problem to develop the relaxation theory in the case of extended-value integrands. Then we discuss applications of the general relaxation theory to some concrete cases, in particular to the theory of strong materials.

KW - extended-valued integrand

KW - lower semicontinuity

KW - relaxation

KW - strong materials

KW - W-quasi-convexity

KW - ENERGY

KW - MINIMA

KW - CALCULUS

KW - GRADIENT

KW - NONLINEAR ELASTICITY

KW - INTEGRALS

KW - GROWTH

KW - W-1;p-quasi-convexity

KW - LOWER SEMICONTINUITY

KW - CONVERGENCE

UR - http://www.scopus.com/inward/record.url?scp=85045749790&partnerID=8YFLogxK

U2 - 10.1017/S0308210518000082

DO - 10.1017/S0308210518000082

M3 - Article

AN - SCOPUS:85045749790

VL - 148

SP - 1029

EP - 1047

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 5

ER -

ID: 12799146