| Title:
|
A note on equality of functional envelopes (English) |
| Author:
|
Kružík, Martin |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
128 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
169-178 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
extreme points |
| Keyword:
|
polyconvexity |
| Keyword:
|
quasiconvexity |
| Keyword:
|
rank-1 convexity |
| Keyword:
|
lower semicontinuous function |
| MSC:
|
49J10 |
| MSC:
|
49J45 |
| MSC:
|
52A05 |
| MSC:
|
52A20 |
| idZBL:
|
Zbl 1028.49007 |
| idMR:
|
MR1995570 |
| DOI:
|
10.21136/MB.2003.134039 |
| . |
| Date available:
|
2009-09-24T22:08:13Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134039 |
| . |
| Reference:
|
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| . |
