# A note on equality of functional envelopes

Mathematica Bohemica (2003)

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

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topKružík, 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 -

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