Lower subdifferentiability and integration (Q1602981)

This well written article is devoted to the question of integration of a multivalued operator \(T:X\to 2^{X^*}\), i.e., the problem of finding a function \(f\) such that, for a suitable notion of subdifferential, \(T\subset \partial f\). In this paper, the case where \(T\) is a \((L(x_0))\) multifunction with respect to some \(x_0\in \operatorname {Dom}T\), \(f\) is quasiconvex and \(\partial\) is the lower subdifferential \(\partial ^{<}\) is considered. Also, the density of the domains of subdifferential operators is characterized.