A note on equality of functional envelopes

Martin Kružík

Mathematica Bohemica (2003)

  • Volume: 128, Issue: 2, page 169-178
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Kružík, Martin. "A note on equality of functional envelopes." Mathematica Bohemica 128.2 (2003): 169-178. <http://eudml.org/doc/249235>.

@article{Kružík2003,
abstract = {We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in $\mathbb \{R\}^\{m\times n\}$, $\min (m,n)\le 2$, 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.},
author = {Kružík, Martin},
journal = {Mathematica Bohemica},
keywords = {extreme points; polyconvexity; quasiconvexity; rank-1 convexity; lower semicontinuous function; extreme points; polyconvexity; quasiconvexity; rank-1 convexity; lower semicontinuous function},
language = {eng},
number = {2},
pages = {169-178},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on equality of functional envelopes},
url = {http://eudml.org/doc/249235},
volume = {128},
year = {2003},
}

TY - JOUR
AU - Kružík, Martin
TI - A note on equality of functional envelopes
JO - Mathematica Bohemica
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 128
IS - 2
SP - 169
EP - 178
AB - We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in $\mathbb {R}^{m\times n}$, $\min (m,n)\le 2$, 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.
LA - eng
KW - extreme points; polyconvexity; quasiconvexity; rank-1 convexity; lower semicontinuous function; extreme points; polyconvexity; quasiconvexity; rank-1 convexity; lower semicontinuous function
UR - http://eudml.org/doc/249235
ER -

References

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