In this paper we show that the functions which are used in the characterization of the -closure or the -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.
Cite this article
M. Miettinen, Uldis Raitums, On -Regularity of Functions that Define -Closure. Z. Anal. Anwend. 20 (2001), no. 1, pp. 203–214