Coron, Jean-Michel Image de la somme de deux sous diffĂ©rentiels. (French) Zbl 0533.46029 Boll. Unione Mat. Ital., V. Ser., A 17, 161-166 (1980). H. Brezis and A. Haraux [Isr. J. Math. 23, 165-186 (1976; Zbl 0323.47041)] showed, for suitable convex functions \(\phi\), \(\psi\) with domains in a real Hilbert space and with subdifferentials \(\partial \phi\), \(\partial \psi\), that if \(\partial \phi +\partial \psi\) is maximal monotone then the range of \(\partial(\phi +\psi)\) is ’nearly equal’ to the sum of the ranges of \(\partial \phi\) and \(\partial \psi\), in the sense that these two sets have the same closure and the same interior. In this note, the hypothesis thatt \(\partial \phi +\partial \psi\) be maximal monotone is shown to be superfluous for equality of the closures but not superfluous for equality of the interiors. Reviewer: J.D.Weston Cited in 1 Document MSC: 46G05 Derivatives of functions in infinite-dimensional spaces 47A55 Perturbation theory of linear operators Keywords:subdifferential; convex functions; maximal monotone Citations:Zbl 0323.47041 PDFBibTeX XMLCite \textit{J.-M. Coron}, Boll. Unione Mat. Ital., V. Ser., A 17, 161--166 (1980; Zbl 0533.46029)