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Necessary and sufficient conditions for isotropic rank-one convex functions in dimension 2

✍ Scribed by Gilles Aubert

Publisher
Springer Netherlands
Year
1995
Tongue
English
Weight
527 KB
Volume
39
Category
Article
ISSN
0374-3535

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✦ Synopsis

We provide some new necessary and sufficient conditions for regular isotropic rank-one convex functions on M + = {2 x 2 matrices such that det M >~ 0}. It is well known that isotmpic functions W(M) can be written as W(M) = G(AI, ),2) where Ai are the singular values of M.

One of these conditions allows us to understand better the gap between the rank-one convexity and the quasiconvexity.

πŸ“œ SIMILAR VOLUMES

On a class of Besicovitch functions to h
On a class of Besicovitch functions to have exact box dimension: A necessary and sufficient condition
✍ S. P. Zhou; G. L. He πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 111 KB

## Abstract Let 1 < __s__ < 2, __Ξ»~k~__ > 0 with __Ξ»~k~__ β†’ ∞ satisfy __Ξ»__~__k__+1~/__Ξ»~k~__ β‰₯ __Ξ»__ > 1. For a class of Besicovich functions __B__(__t__) = $ \sum ^{\infty} \_{k=1} \, \lambda ^{s-2} \_{k} $ sin __Ξ»~k~t__, the present paper investigates the intrinsic relationship between box dimen