Geodesic
A note on equality of functional envelopes
Mathematica Bohemica, Tome 128 (2003) no. 2, pp. 169-178
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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 $\mathbb{R}^{m\times n}$, $\min (m,n)\le 2$, 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.
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 
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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

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