By means of a center manifold analysis we investigate the averaged mean curvature flow near spheres. In particular, we show that there exist global solutions to this flow starting from non-convexâ€¦ (More)

Let X be a Banach space and let A be a closed linear operator on X. It is shown that the abstract Cauchy problem uÌ‡(t) + Au(t) = f (t), t > 0, u(0) = 0, enjoys maximal regularity in weightedâ€¦ (More)

The Willmore flow leads to a quasilinear evolution equation of fourth order. We study existence, uniqueness and regularity of solutions. Moreover, we prove that solutions exist globally and convergeâ€¦ (More)

We show existence and uniqueness of classical solutions for the motion of immersed hypersurfaces driven by surface diffusion. If the initial surface is embedded and close to a sphere, we prove thatâ€¦ (More)

In this paper we establish a geometric theory for abstract quasilinear parabolic equations. In particular, we study existence, uniqueness, and continuous dependence of solutions. Moreover, we giveâ€¦ (More)

It is shown that surface tension effects on the free boundary are regularizing for Hele-Shaw models. This implies, in particular, existence and uniqueness of classical solutions for a large class ofâ€¦ (More)

We study the qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling. It is shown that these problems generateâ€¦ (More)

This paper is concerned with the motion of an incompressible fluid in a rigid porous medium of infinite extent. The fluid is bounded below by a fixed, impermeable layer and above by a free surfaceâ€¦ (More)

In this paper we consider a free boundary problem that describes the motion of two viscous incompressible capillary Newtonian fluids. The fluids are separated by an interface that is unknown and hasâ€¦ (More)