Moving interfaces–and in the stationary case, free boundaries–are ubiquitous in our
environment and daily life. They are at the basis of many physical, chemical, and also …

The primary objective of this monograph is to develop an elementary and se-containedapproachtothemathematicaltheor…
? uid n in a domain? of the Euclidean spaceR, described by the equations of Navier-Stokes …

This book deals with evolutionary systems whose equation of state can be formulated as a
linear Volterra equation in a Banach space. The main feature of the kernels involved is that …

The foundations of this outstanding book series were laid in 1944. Until the end of the
1970s, a total of 77 volumes appeared, including works of such distinguished …

In Section 2.1 the basic theory of sectorial operators is developed, including examples and
the concept of sectorial approximation. In Section 2.2 we introduce some notation for certain …

The property of maximal $ L_p $-regularity for parabolic evolution equations is investigated
via the concept of $\mathcal R $-sectorial operators and operator-valued Fourier multipliers …

We apply an abstract perturbation theorem to derive global in time L q estimates for the
Cauchy problem and L q− L s estimates for the nonstationary Stokes equations in exterior …

In these lecture notes we report on recent breakthroughs in the functional analytic approach
to maximal regularity for parabolic evolution equations, which set off a wave of activity in the …

This book makes available to researchers and advanced graduates a simple and direct
presentation of the fundamental aspects of the theory of fractional powers of non-negative …

In this paper, we give a general definition for f (T) when T is a linear operator acting in a
Banach space, whose spectrum lies within some sector, and which satisfies certain …