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Polyconvex function

Known as: Polyconvexity 
In mathematics, the notion of polyconvexity is a generalization of the notion of convexity for functions defined on spaces of matrices. Let Mm×n(K… 
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Related topics

Related topics

3 relations

Broader (1)

Convex analysis
Convex functionDirect method in the calculus of variations

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2020
2020
Gradient Polyconvexity in Evolutionary Models of Shape-Memory Alloys
We show the existence of an energetic solution to a model of shape-memory alloys in which the elastic energy is described by… 
2018
2018
Again anti-plane shear
We reconsider anti-plane shear deformations of the form $\varphi(x)=(x_1,\,x_2,\,x_3+u(x_1,x_2))$ based on prior work of Knowles… 
2018
2018
More on Anti-plane Shear
We reconsider anti-plane shear deformations based on prior work of Knowles and relate the existence of anti-plane shear… 
2018
2018
3 The classical full equilibrium approach
We reconsider anti-plane shear deformations of the form φ(x) = (x1, x2, x3 + u(x1, x2)) based on prior work of Knowles and relate… 
Review
2016
Review
2016
Weak lower semicontinuity of integral functionals and applications
Minimization is a reoccurring theme in many mathematical disciplines ranging from pure to applied ones. Of particular importance… 
2010
2010
Curvature Bounds for Neighborhoods of Self-Similar Sets
In some recent work, fractal curvatures C^f_k(F) and fractal curvature measures C^f_k(F, .), k = 0, ..., d, have been determined… 
2006
2006
Contact between nonlinearly elastic bodies
We study the contact between nonlinearly elastic bodies by variational methods. After the formulation of the mechanical problem… 
2006
2006
Anisotropic Materials which Can be Modeled by Polyconvex Strain Energy Functions
Polyconvexity is a property of the strain energy function which guarantees existence of solutions to boundary value problems. It… 
2003
2003
On Artin's Braid Group And Polyconvexity In The Calculus Of Variations
Let Ω ⊂ R2 be a bounded Lipschitz domain and let F:Ω×R+2×2→R be a Carathèodory integrand such that F(x, ·) is polyconvex for L2‐a… 
2002
2002
An O(n) invariant rank 1 convex function that is not polyconvex
An O(n) invariant nonnegative rank 1 convex function of linear growth is given that is not polyconvex. This answers a recent… 
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