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Maximal regularity for nonautonomous evolution Institut fur Mathematik,

Summary: Maximal regularity for nonautonomous evolution
H. Amann
Institut f˜ur Mathematik,
Universit˜at Z˜urich, Winterthurerstr. 190, CH--8057 Z˜urich, Switzerland
e­mail: amann@math.unizh.ch
To Antonio Ambrosetti for his 60 th birthday
We derive su#cient conditions, perturbation theorems in particular, for nonau­
tonomous evolution equations to possess the property of maximal Lp regularity.
1991 Mathematics Subject Classification. 35K90, 47D06.
Key words. Maximal regularity, perturbation theorems, nonautonomous parabolic evolution equations.
1 Introduction
Let E 0 and E 1 be Banach spaces such that E 1 is continuously and densely embedded
in E 0 . Suppose that J is a nontrivial compact subinterval of R + containing zero,
and 1 < p < #. Then
W 1
p # J, (E 1 , E 0 ) # := W 1
p (J, E 0 ) # L p (J, E 1 ) (1.1)
and W 1


Source: Amann, Herbert - Institut für Mathematik, Universität Zürich


Collections: Mathematics