Heriot-Watt Mathematics Report Series
HWM99-69, 30 Jan 2000
Regularity of quasiconvex envelopes
J.M. Ball, B Kirchheim and J Kristensen
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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