On semiconvexity properties of rotationally invariant functions in two dimensions

Title:

On semiconvexity properties of rotationally invariant functions in two dimensions

Creator:

Šilhavý, Miroslav

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:cc4c49c8-12bc-420f-8916-5e7eda8d7ad0
uuid:cc4c49c8-12bc-420f-8916-5e7eda8d7ad0

Subject:

semiconvexity, rank 1 convexity, polyconvexity, convexity, and rotational invariance

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $f$ be a function defined on the set ${\mathbf M}^{2\times 2}$ of all $2$ by $2$ matrices that is invariant with respect to left and right multiplications of its argument by proper orthogonal matrices. The function $f$ can be represented as a function $\tilde{f}$ of the signed singular values of its matrix argument. The paper expresses the ordinary convexity, polyconvexity, and rank 1 convexity of $f$ in terms of its representation $\tilde{f}.$

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

559-571

Source:

Czechoslovak Mathematical Journal | 2004 Volume:54 | Number:3

Harvested from:

CDK

Metadata only:

false