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Zeitschrift für Analysis und ihre Anwendungen

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Volume 20, Issue 1, 2001, pp. 203–214
DOI: 10.4171/ZAA/1011

Published online: 2001-03-31

On $C^1$-Regularity of Functions that Define $G$-Closure

M. Miettinen[1] and Uldis Raitums[2]

(1) University of Jyväskylä, Finland
(2) University of Latvia, Riga, Latvia

In this paper we show that the functions which are used in the characterization of the $G$-closure or the $G_\theta$-closure of sets of matrices are continuously differentiable. These regularity results are based on the observation by Ball, Kirchheim and Kristensen [1] that separate convexity and upper semidifferentiability imply continuous differentiability.

Keywords: Homogenization, $G$-closure, quasiconvexity

Miettinen M., Raitums Uldis: On $C^1$-Regularity of Functions that Define $G$-Closure. Z. Anal. Anwend. 20 (2001), 203-214. doi: 10.4171/ZAA/1011