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On Legendre and Weierstrass conditions in one-dimensional variational problems. / Sychev, M. A.; Sycheva, N. N.

In: Journal of Convex Analysis, Vol. 24, No. 1, 01.01.2017, p. 123-133.

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

Harvard

Sychev, MA & Sycheva, NN 2017, 'On Legendre and Weierstrass conditions in one-dimensional variational problems', Journal of Convex Analysis, vol. 24, no. 1, pp. 123-133.

APA

Sychev, M. A., & Sycheva, N. N. (2017). On Legendre and Weierstrass conditions in one-dimensional variational problems. Journal of Convex Analysis, 24(1), 123-133.

Vancouver

Sychev MA, Sycheva NN. On Legendre and Weierstrass conditions in one-dimensional variational problems. Journal of Convex Analysis. 2017 Jan 1;24(1):123-133.

Author

Sychev, M. A. ; Sycheva, N. N. / On Legendre and Weierstrass conditions in one-dimensional variational problems. In: Journal of Convex Analysis. 2017 ; Vol. 24, No. 1. pp. 123-133.

BibTeX

@article{d24ec370f16549a78fec9d53a76b0078,
title = "On Legendre and Weierstrass conditions in one-dimensional variational problems",
abstract = "In this paper we show that classical conditions of Legendre and Weierstrass characterize lower semicontinuity of the correspondent integral functional in appropriate classes of functions. A strengthened version of these conditions characterize the property of the functional of convergence in energy.",
keywords = "Convergence in energy, Convexity at a point, Integral functionals, Legendre condition, Lower semicontinuity, Strict convexity at a point, Weierstrass condition, Young measures",
author = "Sychev, {M. A.} and Sycheva, {N. N.}",
note = "Publisher Copyright: {\textcopyright} Heldermann Verlag.",
year = "2017",
month = jan,
day = "1",
language = "English",
volume = "24",
pages = "123--133",
journal = "Journal of Convex Analysis",
issn = "0944-6532",
publisher = "Heldermann Verlag",
number = "1",

}

RIS

TY - JOUR

T1 - On Legendre and Weierstrass conditions in one-dimensional variational problems

AU - Sychev, M. A.

AU - Sycheva, N. N.

N1 - Publisher Copyright: © Heldermann Verlag.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In this paper we show that classical conditions of Legendre and Weierstrass characterize lower semicontinuity of the correspondent integral functional in appropriate classes of functions. A strengthened version of these conditions characterize the property of the functional of convergence in energy.

AB - In this paper we show that classical conditions of Legendre and Weierstrass characterize lower semicontinuity of the correspondent integral functional in appropriate classes of functions. A strengthened version of these conditions characterize the property of the functional of convergence in energy.

KW - Convergence in energy

KW - Convexity at a point

KW - Integral functionals

KW - Legendre condition

KW - Lower semicontinuity

KW - Strict convexity at a point

KW - Weierstrass condition

KW - Young measures

UR - http://www.scopus.com/inward/record.url?scp=85015089491&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85015089491

VL - 24

SP - 123

EP - 133

JO - Journal of Convex Analysis

JF - Journal of Convex Analysis

SN - 0944-6532

IS - 1

ER -

ID: 10274288