On some evolution equations of subdifferential operators
Kenji Maruo · Proceedings of the Japan Academy Series A Mathematical Sciences · 1975
1o Introduction.In this paper we are concerned with nonlinearin a real Hilbert space H.Here for each fixed t, 3t is subdifferential of a lower semicontinuous convex function t from H into (--c, and A(t) is a monotone, single valued and hemicontinuous operator which is perturbation in a sense.The effective domain of t defined by {u e H" t(u) + }=D is independent of t.We denote the inner product and the norm in H by (,) and respectively.Let T be a positive constant. We assume the following conditions or t and A(t).A-(l).For every r 0 there exists a positive constant L(r) such that t(u)--S(u)]L(r) ]h(t)--h(s)] {t(u) + i} hold if 0s, t T, u e D and I]u r, where h(t) is a continuous function with bounded total variation.