Regularity of quasiconvex envelopes
John M. Ball, Bernd Kirchheim,and Jan Kristensen
Contact the author: Please use for correspondence this email.
Submission date: 22. Dec. 1999
published in: Calculus of variations and partial differential equations, 11 (2000) 4, p. 333-359
DOI number (of the published article): 10.1007/s005260000041
Download full preprint: PDF (420 kB), PS ziped (181 kB)
We prove that the quasiconvex envelope of a differentiable function which satisfies natural growth conditions at infinity is a function. Without the growth conditions the result fails in general. We also obtain results on higher regularity (in the sense of ) and similar results for other types of envelopes, including polyconvex and rank-1 convex envelopes.