A note on equality of functional envelopes

Title:

A note on equality of functional envelopes

Creator:

Kružík, Martin

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:ea62543d-13e9-4009-ac47-ef1cc2f52bce
uuid:ea62543d-13e9-4009-ac47-ef1cc2f52bce
doi:10.21136/MB.2003.134039

Subject:

extreme points, polyconvexity, quasiconvexity, rank-1 convexity, and lower semicontinuous function

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in R m×n , min(m, n) ≤ 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.

Language:

English

Rights:

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

Coverage:

169-178

Source:

Mathematica bohemica | 2003 Volume:128 | Number:2

Harvested from:

CDK

Metadata only:

false