Calculus of Variations and Partial Differential Equations

, Volume 11, Issue 4, pp 333–359

Regularity of quasiconvex envelopes

  • John M. Ball
  • Bernd Kirchheim
  • Jan Kristensen
Original article

DOI: 10.1007/s005260000041

Cite this article as:
Ball, J., Kirchheim, B. & Kristensen, J. Calc Var (2000) 11: 333. doi:10.1007/s005260000041

Abstract.

We prove that the quasiconvex envelope of a differentiable function which satisfies natural growth conditions at infinity is a \(C^1\) function. Without the growth conditions the result fails in general. We also obtain results on higher regularity (in the sense of \(C^{1,\alpha}_{\rm loc}\)) and similar results for other types of envelopes, including polyconvex and rank-1 convex envelopes.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • John M. Ball
    • 1
  • Bernd Kirchheim
    • 2
  • Jan Kristensen
    • 1
  1. 1.Mathematical Institute, University of Oxford, OX1 3LB Oxford, EnglandGB
  2. 2.Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstr. 22–26, 04103 Leipzig, GermanyDE