Abstract.
This paper deals with a parabolic problem u′ (t)=A (t) u (t)+f (t), u (0)=x, on a Banach space X. We establish maximal Lp regularity, p ∈[1,+∞[, on a suitable extrapolation space of X. As a consequence we obtain weak solutions that have the same regularity of the mild solutions in the autonomous case.
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Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday
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Blasio, G.D. Maximal Lp regularity for nonautonomous parabolic equations in extrapolation spaces1. J. evol. equ. 6, 229–245 (2006). https://doi.org/10.1007/s00028-006-0241-3
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DOI: https://doi.org/10.1007/s00028-006-0241-3