Abstract
We consider non-autonomous evolutionary problems of the form
on \({L^{2}([0, T]; H)}\), where H is a Hilbert space. We do not assume that the domain of the operator A(t) is constant in time t, but that A(t) is associated with a sesquilinear form \({\mathfrak{a}(t)}\). Under sufficient time regularity of the forms \({\mathfrak{a}(t)}\), we prove well-posedness with maximal regularity in \({L^{2}([0, T]; H)}\). Our regularity assumption is significantly weaker than those from previous results inasmuch as we only require a fractional Sobolev regularity with arbitrary small Sobolev index.
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Dier, D., Zacher, R. Non-autonomous maximal regularity in Hilbert spaces. J. Evol. Equ. 17, 883–907 (2017). https://doi.org/10.1007/s00028-016-0343-5
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DOI: https://doi.org/10.1007/s00028-016-0343-5