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 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 …

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 explores new difference schemes for approximating the solutions of regular and
singular perturbation boundary-value problems for PDEs. The construction is based on the …

We develop a very general operator-valued functional calculus for operators with an H^∞-
calculus. We then apply this to the joint functional calculus of two sectorial operators when …

More than 13 years have passed since the fundamental survey [16] was prepared, which, as
the author intended, should have been the first part of a large work devoted to abstract …

This is a survey on recent developments of the theory of one-parameter semigroups and
evolution equations with special emphasis on functional calculus and kernel estimates. Also …

Given a closed linear operator on aUMD-space, we characterize maximal regularity of the
non-homogeneous problem u+ Au= f with periodic boundary conditions in terms of R …

This review paper is devoted to the numerical analysis of abstract differential equations in
Banach spaces. Most of the finite-difference, finite-element, and projection methods can be …

Let is a UMD-space. Introducing stronger conditions we obtain a periodic Fourier multiplier
theorem which is valid without restriction on the indices or the space (which is analogous to …