Maximal Regularity for Nonautonomous Evolution Equations

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Quasilinear parabolic problems via maximal regularity (2005, methodology): “By combining this proposition with the perturbation theorems of [5] we easily obtain sufficient conditions for operators B with ‘fully occupied’ matrices [Bjk] to possess the property of maximal L~ p regularity, provided the subdiagonal entries Bj,k, 1 ≤ j < k ≤ N , are suitably ‘subordinate’.”
Maximal Regularity for Non-autonomous Equations with Measurable Dependence on Time (2014, background): “gularity (see [53, 54] and [29]), but their example is not a diﬀerential operator. In the case t → A(t) is (piecewise) continuous, one can study maximal Lpregularity using perturbation arguments (see [5, 7, 82]). In particular, in [82], it was shown that maximal Lp-regularity of (1.1) is equivalent ”