Geodesic
On Legendre and Weierstrass Conditions in One-Dimensional Variational Problems
Journal of convex analysis, Tome 24 (2017) no. 1, pp. 123-133
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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.
Mots-clés : Integral functionals, Legendre condition, Weierstrass condition, convexity at a point, strict convexity at a point, lower semicontinuity, convergence in energy, Young measures 
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     author = {M. A. Sychev and N. N. Sycheva},
     title = {On {Legendre} and {Weierstrass} {Conditions} in {One-Dimensional} {Variational} {Problems}},
     journal = {Journal of convex analysis},
     pages = {123--133},
     year = {2017},
     volume = {24},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a9/}
}
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M. A. Sychev; N. N. Sycheva. On Legendre and Weierstrass Conditions in One-Dimensional Variational Problems. Journal of convex analysis, Tome 24 (2017) no. 1, pp. 123-133. http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a9/