Summary: Maximal regularity for nonautonomous evolution
Institut f˜ur Mathematik,
Universit˜at Z˜urich, Winterthurerstr. 190, CH--8057 Z˜urich, Switzerland
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.
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
p # J, (E 1 , E 0 ) # := W 1
p (J, E 0 ) # L p (J, E 1 ) (1.1)
and W 1