Geodesic
Regular Maximal Monotone Operators and the Sum Theorem
Journal of convex analysis, Tome 7 (2000) no. 1, pp. 115-128.

Voir la notice de l'article provenant de la source Heldermann Verlag

In this note, which is a continuation of a previous paper of the authors [Set-Valued Analysis 6 (1998) 302-312], we study two classes of maximal monotone operators on general Banach spaces which we call C0 (resp. C1)-regular. All maximal monotone operators on a reflexive Banach space, all subdifferential operators, and all maximal monotone operators with domain the whole space are C1-regular and all linear maximal monotone operators are C0-regular. We prove that the sum of a C0 (or C1)-regular maximal monotone operator with a maximal monotone operator which is locally inf bounded and whose domain is closed and convex is again maximal monotone provided that they satisfy a certain "dom--dom" condition. From this result one can obtain most of the known sum theorem type results in general Banach spaces. We also prove a local boundedness type result for pairs of monotone operators. 
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A. Verona; M. E. Verona. Regular Maximal Monotone Operators and the Sum Theorem. Journal of convex analysis, Tome 7 (2000) no. 1, pp. 115-128. http://geodesic.mathdoc.fr/item/JCA_2000_7_1_JCA_2000_7_1_a5/