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## Regularity of quasiconvex envelopes

### 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

Topics: Partial differential equations, Calculus of variations and optimal control
Year: 2000
DOI identifier: 10.1007/s005260000041
OAI identifier: oai:generic.eprints.org:196/core69

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