Regularity of quasiconvex envelopes

John M. Ball, Bernd Kirchheim, and Jan Kristensen
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Submission date: 22. Dec. 1999
Pages: 25
published in: Calculus of variations and partial differential equations, 11 (2000) 4, p. 333-359 
DOI number (of the published article): 10.1007/s005260000041
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Abstract:
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.