Abstract
We consider the problem of maximal regularity for non-autonomous Cauchy problems ¨ u(t) + B(t) ˙ u(t) + A(t)u(t) = f (t) (t ∈ [0, τ ]), u(0) = u 0 , ˙ u(0) = u 1. Here, the time dependent operator A(t) is bounded from V to V ′ and B(t) is associated with a family of sesquilinear forms with domain V. We prove maximal L p-regularity results and other regularity properties for the solutions of the previous problems under minimal regularity assumptions on the operators.
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