Characterization of polyconvex isotropic functions
Abstract
Abstract Polyconvexity is an important concept in the analysis of energies related to elasticity. A function $$W :\mathbb {R}^{d\times d} \rightarrow \mathbb {R}$$ W : R d × d → R is called polyconvex if it can be written as a convex function in the minors of the argument. We show that for isotropic functions it suffices to consider diagonal matrices. For $$d=3$$ d = 3 , this leads to a dimension reduction for the convex representative of W from $$\mathbb {R}^{19}$$ R 19 to $$\mathbb {R}^7$$ R 7 . Moreover, we present a new result for the polyconvexity of functions formulated in the principal invariant of the left or right stretch tensor.
Fields of Study & Subjects
Mathematical Inequalities and Applications
Analytic and geometric function theory
Holomorphic and Operator Theory
Publication details
- Journal / source
- Calculus of Variations and Partial Differential Equations
- Publisher
- Springer Science and Business Media LLC
- Volume
- 65
- Issue
- 4
- Publication date
- 28 February 2026
- Language
- EN