On lower-semicontinuity of variational integrals

Šverák, Vladimír

Displaying similar documents to “On lower-semicontinuity of variational integrals”

On the non-locality of quasiconvexity

Jan Kristensen (1999)

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Lower semicontinuity of L∞ functionals

E. N. Barron, R. R. Jensen, C. Y. Wang (2001)

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A note on equality of functional envelopes

Martin Kružík (2003)

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We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in $ℝ^{m \times n}$ , $min (m, n) \leq 2$ , then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit convexity assumptions on the quasiconvex (polyconvex) envelope.

Theorems on lower semicontinuity and relaxation for integrands with fast growth.

Sychev, M.A. (2005)

Sibirskij Matematicheskij Zhurnal

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Critique of "Two-dimensional examples of rank-one convex functions that are not quasiconvex" by M. K. Benaouda and J. J. Telega

Patrizio Neff (2005)

Annales Polonici Mathematici

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It is noted that the examples provided in the paper "Two-dimensional examples of rank-one convex functions that are not quasiconvex" by M. K. Benaouda and J. J. Telega, Ann. Polon. Math. 73 (2000), 291-295, contain unrecoverable errors.

New convexity conditions in the calculus of variations and compensated compactness theory

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 $I_{f} (u) = \int_{Ω} f (u) d x$ where $u$ 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 $Λ$ -convexity condition for the integrand $f$ 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...