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Maximal regularity and quasilinear evolution equations Herbert Amann
 

Summary: Maximal regularity and quasilinear evolution equations
Herbert Amann
1. Abstract theory
Let E 0 and E 1 be Banach spaces such that E 1
d
## E 0 , set J := J T0 := [0, T 0 ) for
some fixed positive T 0 , and suppose that 1 < p < #. Put
W 1
p (J) := W 1
p # J, (E 1 , E 0 ) # := L p (J, E 1 ) # W 1
p ( š
J , E 0 ).
Then
B # L# # J, L(E 1 , E 0 ) #
possesses the property of maximal L p regularity on J with respect to (E 1 , E 0 )
if the map
W 1
p (J) # L p (J, E 0 ) ×E, u ## # —
u +Bu,u(0) #
is a bounded isomorphism, where E is the real interpolation space (E 0 , E 1 ) 1/p # ,p

  

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

 

Collections: Mathematics