Regularity of quasiconvex envelopes - Ball, J; Kirchheim, B; Kristensen, J (2000)
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 $C^{1,α}_{\rm loc}$) and similar results for other types of envelopes, including polyconvex and rank-1 convex envelopes.