Some examples of rank one convex functions in dimension two
From MaRDI portal
Publication:3209723
DOI10.1017/S0308210500024318zbMath0722.49018OpenAlexW2114821056MaRDI QIDQ3209723
Jacques Douchet, Wilfrid Gangbo, Bernard Dacorogna, Jacques Rappaz
Publication date: 1990
Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s0308210500024318
Methods involving semicontinuity and convergence; relaxation (49J45) Convexity of real functions in one variable, generalizations (26A51)
Related Items
On the different notions of convexity for rotationally invariant functions, Numerical evidence towards a positive answer to Morrey's problem, Relaxation of some functionals of the calculus of variations, Numerical approaches for investigating quasiconvexity in the context of Morrey's conjecture, Numerical optimization and quasiconvexity, A polyconvexity condition in dimension two, On the condition of tetrahedral polyconvexity, arising from calculus of variations, The exponentiated Hencky-logarithmic strain energy. II: Coercivity, planar polyconvexity and existence of minimizers, An example of a quasiconvex function that is not polyconvex in two dimensions, The quasiconvexification of a cubic polynomial at the origin, NONLINEARLY ELASTIC THIN PLATE MODELS FOR A CLASS OF OGDEN MATERIALS: I, Some numerical methods for the study of the convexity notions arising in the calculus of variations, Finding new families of rank-one convex polynomials, On the relation between polyconvexity and rank-one convexity in nonlinear elasticity, Some remarks on quasiconvexity and rank-one convexity, New convexity conditions in the calculus of variations and compensated compactness theory
Cites Work
- Unnamed Item
- \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
- Quasiconvex quadratic forms in two dimensions
- On the ellipticity of the equations of nonlinear elastostatics for a special material
- Die Darstellung biquadratischer Formen als Summen von Quadraten mit Anwendung auf die Variationsrechnung
- Quasi-convexity and the lower semicontinuity of multiple integrals
- Optimal design and relaxation of variational problems, I
- Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids
- A quadratic form problem in the calculus of variations
- A theorem on quadratic forms
- Direct methods in the calculus of variations
