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Four applications of majorization to convexity in the calculus of variations

โœ Scribed by Marius Buliga

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
184 KB
Volume
429
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

The resemblance between the Horn-Thompson theorem and a recent theorem by Dacorogna-Marcellini-Tanteri indicates that Schur-convexity and the majorization relation are relevant for applications in the calculus of variations and its related notions of convexity, such as rank one convexity or quasiconvexity.

In Theorem 6.6, we give simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on the set of matrices with positive determinant.

Majorization is used in order to give a very short proof of a theorem of Thompson and Freede [R.C.

๐Ÿ“œ SIMILAR VOLUMES

The Direct Method in the Calculus of Var
The Direct Method in the Calculus of Variations for Convex Bodies
โœ David Jerison ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 435 KB

The purpose of this paper is to calculate the first variation of capacity and of the lowest eigenvalue for the Dirichlet problem in convex domains in R N . These formulas are well known in the smooth case and are due to Poincare and Hadamard, respectively. The point is to prove them in sufficient ge