On the different notions of convexity for rotationally invariant functions

DOI10.5802/afst.762zbMath0828.49016OpenAlexW1964872188MaRDI QIDQ1327529

Bernard Dacorogna, Hideyuki Koshigoe

Publication date: 7 January 1996

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_1993_6_2_2_163_0

zbMATH Keywords

polyconvexityquasi-convexityrotationally invariant functionsconvexity conditionsrank-one convexity

Mathematics Subject Classification ID

Existence theories in calculus of variations and optimal control (49J99)

Related Items (13)

Extremal problems involving isotropic sets and functions on spaces of rectangular matrices ⋮ Orbital equations for extremal problems under various invariance assumptions ⋮ A note on invariant functions ⋮ The exponentiated Hencky-logarithmic strain energy. I: Constitutive issues and rank-one convexity ⋮ A polyconvexity condition in dimension two ⋮ The exponentiated Hencky-logarithmic strain energy. II: Coercivity, planar polyconvexity and existence of minimizers ⋮ Relaxation results for functions depending on polynomials changing sign on rank-one matrices ⋮ Convex \(\mathrm{SO}(N) \times \mathrm{SO}(n)\)-invariant functions and refinements of von Neumann's inequality ⋮ The quasiconvex envelope of conformally invariant planar energy functions in isotropic hyperelasticity ⋮ On Semiconvexity Properties of Rotationally Invariant Functions in Two Dimensions ⋮ Quasiconvex relaxation of isotropic functions in incompressible planar hyperelasticity ⋮ Characterizations of symmetric polyconvexity ⋮ Convex analysis on Cartan subspaces.

Cites Work

• An example of a quasiconvex function that is not polyconvex in two dimensions
• Convexity conditions and existence theorems in nonlinear elasticity
• Integral estimates for null Lagrangians
• Some examples of rank one convex functions in dimension two
• Quasiconvex functions with subquadratic growth
• Rank-one convexity does not imply quasiconvexity
• Direct methods in the calculus of variations
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