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

M. Miettinen; Uldis Raitums

doi:10.4171/zaa/1011

JournalszaaVol. 20, No. 1pp. 203–214

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

M. Miettinen
University of Jyväskylä, Finland
Uldis Raitums
University of Latvia, Riga, Latvia

Download PDF

Abstract

In this paper we show that the functions which are used in the characterization of the $G$ -closure or the $G_{θ}$ -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.

Cite this article

M. Miettinen, Uldis Raitums, On $C^{1}$ -Regularity of Functions that Define $G$ -Closure. Z. Anal. Anwend. 20 (2001), no. 1, pp. 203–214

DOI 10.4171/ZAA/1011