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 …

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 …

The global-in-time existence of bounded weak solutions to a large class of physically
relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure is …

抄録 This survey article discusses various aspects of modeling and analysis of the Ericksen-
Leslie equations describing nematic liquid crystal flow both in the isothermal and non …

We consider the system of Maxwell-Stefan equations which describe multicomponent
diffusive fluxes in non-dilute solutions or gas mixtures. We apply the Perron-Frobenius …

We consider a solution of the Cahn–Hilliard equation or an associated Caginalp problem
with dynamic boundary condition in the case of a general potential and prove that under …

Abstract The well known De Giorgi result on Hölder continuity for solutions of the Dirichlet
problem is re-established for mixed boundary value problems, provided that the underlying …

Local-in-time well-posedness of the initial-boundary value problem for a class of non-
Newtonian Navier–Stokes problems on domains with compact C^3--boundary is proven in …

This work explains how to solve evolution equations via novel iterative-based splitting
methods that efficiently use computational and memory resources. It focuses on systems of …

In this paper we develop a geometric theory for quasilinear parabolic problems in weighted
L p-spaces. We prove existence and uniqueness of solutions as well as the continuous …