On lower-semicontinuity of variational integrals
Šverák, Vladimír
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Šverák, Vladimír
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Jan Kristensen (1999)
Annales de l'I.H.P. Analyse non linéaire
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Kewei Zhang (2001)
ESAIM: Control, Optimisation and Calculus of Variations
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The notion of quasiconvex exposed points is introduced for compact sets of matrices, motivated from the variational approach to material microstructures. We apply the notion to give geometric descriptions of the quasiconvex extreme points for a compact set. A weak version of Straszewicz type density theorem in convex analysis is established for quasiconvex extreme points. Some examples are examined by using known explicit quasiconvex functions.
Leviatan, D., Shevchuk, I. (2002)
Serdica Mathematical Journal
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* Part of this work was done while the second author was on a visit at Tel Aviv University in March 2001 Let f ∈ C[−1, 1] change its convexity finitely many times, in the interval. We are interested in estimating the degree of approximation of f by polynomials, and by piecewise polynomials, which are nearly coconvex with it, namely, polynomials and piecewise polynomials that preserve the convexity of f except perhaps in some small neighborhoods of the points where f changes...
Agrawal, Hukum Chand (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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Krzysztof Chełmiński, Agnieszka Kałamajska (2006)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the lower semicontinuous functional of the form where satisfies a given conservation law defined by differential operator of degree one with constant coefficients. We show that under certain constraints the well known Murat and Tartar’s -convexity condition for the integrand extends to the new geometric conditions satisfied on four dimensional symplexes. Similar conditions on three dimensional symplexes were recently obtained by the second author. New conditions apply...
Shukla, D.P. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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Roberto Dvornicich, Shih Ping Tung, Umberto Zannier (2003)
Acta Arithmetica
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