 
Summary: MAXIMAL REGULARITY AND QUASILINEAR
PARABOLIC BOUNDARY VALUE PROBLEMS
HERBERT AMANN
Institut f˜ur Mathematik
Universit˜at Z˜urich
Winterthurerstr. 190
CH8057 Z˜urich
Switzerland
Email: amann@math.unizh.ch
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.
Introduction
In this paper we consider quasilinear parabolic evolution equations of the
form
—
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
