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.
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Received January 11, 2000/ Accepted January 14, 2000 / Published online June 28, 2000
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Ball, J., Kirchheim, B. & Kristensen, J. Regularity of quasiconvex envelopes. Calc Var 11, 333–359 (2000). https://doi.org/10.1007/s005260000041
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DOI: https://doi.org/10.1007/s005260000041