Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2001-03-31
On $C^1$-Regularity of Functions that Define $G$-ClosureM. Miettinen and Uldis Raitums (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  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