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An example of a \(C^{1,1}\) polyconvex function with no differentiable convex representative.

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Publication:1871547
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DOI10.1016/S1631-073X(02)00015-8zbMath1036.49003MaRDI QIDQ1871547

Jonathan J. Bevan

Publication date: 2003

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)


zbMATH Keywords

subgradientspolyconvex functionconvex representatives


Mathematics Subject Classification ID

Existence theories for free problems in two or more independent variables (49J10) Methods involving semicontinuity and convergence; relaxation (49J45)


Related Items

Singular minimizers of strictly polyconvex functionals in \(\mathbb R^{2 \times 2}\)



Cites Work

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  • Differentiability properties of symmetric and isotropic functions
  • Quasiconvexity and partial regularity in the calculus of variations
  • Convexity conditions and existence theorems in nonlinear elasticity
  • A singular minimizer of a smooth strongly convex functional in three dimensions
  • Regularity of quasiconvex envelopes
  • Singular minimizers of strictly polyconvex functionals in \(\mathbb R^{2 \times 2}\)
  • Convex bodies and convexity on Grassmann cones. I-IV
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