Calculus of Variations and Partial Differential Equations

, Volume 11, Issue 4, pp 333–359

Regularity of quasiconvex envelopes

Authors

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