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Image de la somme de deux sous différentiels. (French) Zbl 0533.46029

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

MSC:

46G05 Derivatives of functions in infinite-dimensional spaces
47A55 Perturbation theory of linear operators

Citations:

Zbl 0323.47041
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