Geodesic
A note on equality of functional envelopes
Mathematica Bohemica, Tome 128 (2003) no. 2, pp. 169-178.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/MB.2003.134039
Classification : 49J10, 49J45, 52A05, 52A20
Keywords: extreme points; polyconvexity; quasiconvexity; rank-1 convexity; lower semicontinuous function 
@article{10_21136_MB_2003_134039,
     author = {Kru\v{z}{\'\i}k, Martin},
     title = {A note on equality of functional envelopes},
     journal = {Mathematica Bohemica},
     pages = {169--178},
     publisher = {mathdoc},
     volume = {128},
     number = {2},
     year = {2003},
     doi = {10.21136/MB.2003.134039},
     mrnumber = {1995570},
     zbl = {1028.49007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134039/}
}
TY  - JOUR
AU  - Kružík, Martin
TI  - A note on equality of functional envelopes
JO  - Mathematica Bohemica
PY  - 2003
SP  - 169
EP  - 178
VL  - 128
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134039/
DO  - 10.21136/MB.2003.134039
LA  - en
ID  - 10_21136_MB_2003_134039
ER  - 
%0 Journal Article
%A Kružík, Martin
%T A note on equality of functional envelopes
%J Mathematica Bohemica
%D 2003
%P 169-178
%V 128
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134039/
%R 10.21136/MB.2003.134039
%G en
%F 10_21136_MB_2003_134039
Kružík, Martin. A note on equality of functional envelopes. Mathematica Bohemica, Tome 128 (2003) no. 2, pp. 169-178. doi : 10.21136/MB.2003.134039. http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134039/

Cité par Sources :