Monotonicity and upper semicontinuity

M. B. Suryanarayana
1976 Bulletin of the American Mathematical Society  
Introduction. We show in this note that set valued maximal monotone operators on a Hilbert space possess the upper semicontinuity property called property (0, introduced by Cesari [2] and used extensively in the existence analysis of optimal control theory. As a particular consequence we conclude rather easily, the known result (see [1] , for example) that maximal monotone operators have closed graph and are thus demiclosed. As a simple application of this to optimal control theory we give an
more » ... istence theorem for a Mayer problem. Details and extensions are found in [5] where we study upper semicontinuity in the context of semiclosure operators of general topology.
doi:10.1090/s0002-9904-1976-14225-5 fatcat:gvv5etkgbbb57mimwqqwldzh5m