| Issue |
ESAIM: M2AN
Volume 38, Number 5, September-October 2004
|
|
|---|---|---|
| Page(s) | 811 - 820 | |
| DOI | https://doi.org/10.1051/m2an:2004040 | |
| Published online | 15 October 2004 | |
Linear convergence in the approximation of rank-one convex envelopes
Department of Mathematics, University of Maryland,
College Park, MD 20742-4015, USA. sba@math.umd.edu.
Received:
27
May
2003
A linearly convergent iterative algorithm that approximates the
rank-1 convex envelope 
of a given function 
,
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.
Mathematics Subject Classification: 65K10 / 74G15 / 74G65 / 74N99
Key words: Nonconvex variational problem / calculus of variations / relaxed variational problems / rank-1 convex envelope / microstructure / iterative algorithm.
© EDP Sciences, SMAI, 2004
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