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Quasiconvex functions can be approximated by quasiconvex polynomials

Published online by Cambridge University Press:  30 January 2008

Sebastian Heinz
Sebastian Heinz*
Affiliation:
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik, DFG-Graduiertenkolleg 1128, Germany; sheinz@mathematik.hu-berlin.de
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Abstract

Let W be a function from the real m×n-matrices to the real numbers. If W is quasiconvex in the sense of the calculus of variations, then we show that W can be approximated locally uniformly by quasiconvex polynomials.

Keywords

Stone-Weierstrass theoremlocally uniform convergence
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 4 , October 2008 , pp. 795 - 801
Copyright
© EDP Sciences, SMAI, 2008

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