Abstract
We study the Cauchy problem for the abstract evolution equation u″(s<+ A(s<u(s<=0. For a.a. s ∃ [0, T], A(s) is an unbounded self-adjoint positive operator in a Hilbert space H, with everywhere defined inverse. The domain of A(s) is allowed to vary with s, and we have tried to make minimal assumptions on the time regularity of the map A(·). We provide results concerning existence, uniqueness and regularity of the solution both from the semigroup and the variational point of view (indeed these are the extremal cases of a continuous family of problems, indexed by a parameter α ∃ [1/2, 1], for which the approach may be easily unified).
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