Displaying similar documents to “Some numerical methods for the study of the convexity notions arising in the calculus of variations”

Linear convergence in the approximation of rank-one convex envelopes

Sören Bartels (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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A linearly convergent iterative algorithm that approximates the rank-1 convex envelope f r c of a given function f : ℝ n × m → ℝ , i.e. the largest function below f which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington.

A note on equality of functional envelopes

Martin Kružík (2003)

Mathematica Bohemica

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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.