A note on equality of functional envelopes

Martin Kružík

Displaying similar documents to “A note on equality of functional envelopes”

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.

On the structure of quasiconvex hulls

Kewei Zhang (1998)

Annales de l'I.H.P. Analyse non linéaire

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On the non-locality of quasiconvexity

Jan Kristensen (1999)

Annales de l'I.H.P. Analyse non linéaire

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On the quasiconvex exposed points

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.

A complete characterization of invariant jointly rank- convex quadratic forms and applications to composite materials

Vincenzo Nesi, Enrico Rogora (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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The theory of compensated compactness of Murat and Tartar links the algebraic condition of rank- convexity with the analytic condition of weak lower semicontinuity. The former is an algebraic condition and therefore it is, in principle, very easy to use. However, in applications of this theory, the need for an efficient classification of rank- convex forms arises. In the present paper, we define the concept of extremal -forms and characterize them in the rotationally invariant...

Rank 1 convex hulls of isotropic functions in dimension 2 by 2

Miroslav Šilhavý (2001)

Mathematica Bohemica

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Let $f$ be a rotationally invariant (with respect to the proper orthogonal group) function defined on the set $M^{2 \times 2}$ of all $2$ by $2$ matrices. Based on conditions for the rank 1 convexity of $f$ in terms of signed invariants of $𝔸$ (to be defined below), an iterative procedure is given for calculating the rank 1 convex hull of a rotationally invariant function. A special case in which the procedure terminates after the second step is determined and examples of the actual calculations are given. ...