The Mathematical Institute, University of Oxford, Eprints Archive

Regularity of quasiconvex envelopes

Ball, J. M. and Kirchheim, Bernd and Kristensen, Jan (2000) Regularity of quasiconvex envelopes. Calculus of Variations and Partial Differential Equations, 11 (4). pp. 333-359. ISSN 0944-2669 (Paper) 1432-0835 (Online)


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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.

Item Type:Article
Subjects:O - Z > Partial differential equations
A - C > Calculus of variations and optimal control
Research Groups:Oxford Centre for Nonlinear PDE
ID Code:196
Deposited By: John Ball
Deposited On:30 Aug 2005
Last Modified:29 May 2015 18:18

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