Summary: MAXIMAL REGULARITY AND QUASILINEAR
PARABOLIC BOUNDARY VALUE PROBLEMS
Institut f˜ur Mathematik
There is given a sharp existence, uniqueness, and continuity theorem for quasilinear
parabolic evolution equations, based on the concept of maximal Sobolev regularity.
Its power is illustrated by applications to some model problems which are nonlocal
in space and/or time.
In this paper we consider quasilinear parabolic evolution equations of the
u +A(u)u = f(u) in š
J , u(0) = u 0 , (1)
where J := J T0 := [0, T 0 ) for some fixed positive T 0 . We study (1) un