Article
Ufa Mathematical Journal
Volume 9, Number 4, pp. 54-58
On continuity and differentiability of the maximum values of functions
Klyachin V.A.
DOI:10.13108/2017-9-4-54
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This article discusses the functions which are the maximum values of continuous functions on compact subsets of families. These functions are used, for example, in the study of the geometric structure of the equilibrium of different surfaces -- minimal surfaces, surfaces of constant mean curvature, etc. In this paper we find conditions under which such functions are continuous and differentiable.