Topology and geometry of nontrivial rank-one convex hulls for two-by-two matrices

DOI10.1051/cocv:2005036zbMath1108.49010OpenAlexW1974345769WikidataQ59902280 ScholiaQ59902280MaRDI QIDQ3416740

Carl-Friedrich Kreiner, Johannes Zimmer

Publication date: 22 January 2007

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=COCV_2006__12_2_253_0

zbMATH Keywords

Rank-one convexity\(T_4\)-configurations

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)

Related Items (2)

On the condition of tetrahedral polyconvexity, arising from calculus of variations ⋮ Upper semicontinuity of the lamination hull

Uses Software

• Macaulay2

Cites Work

• Unexpected solutions of first and second order partial differential equations
• On functional separately convex hulls
• A constrained sequential-lamination algorithm for the simulation of sub-grid microstructure in martensitic materials.
• Rank-one convex hulls in \(\mathbb R^{2\times 2}\)
• On the Computation of the Rank-One Convex Hull of a Function
• Rank-one convexity does not imply quasiconvexity
• Numerical Computation of Rank-One Convex Envelopes
• Studying Nonlinear pde by Geometry in Matrix Space
• Rigidity for the four gradient problem
• Direct methods in the calculus of variations
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