We prove a general regularity result for fully nonlinear, possibly nonlocal parabolic Cauchy problems under the assumption of maximal regularity for the linearized problem. We apply this result toâ€¦ (More)

Interest is directed to a moving boundary problem with a gradient flow structure which generalizes surface-tension driven Hele-Shaw flow to the case of nonconstant surface tension coefficient takenâ€¦ (More)

We discuss a 2D moving-boundary problem for the Laplacian with Robin boundary conditions in an exterior domain. It arises as model for Hele-Shaw flow of a bubble with kinetic undercoolingâ€¦ (More)

We consider short-time existence, uniqueness, and regularity for a moving boundary problem describing Stokes flow of a free liquid drop driven by surface tension. The surface tension coefficient isâ€¦ (More)

We discuss a moving boundary problem arising from a model of gas ionization in the case of negligible electron diffusion and suitable initial data. It describes the time evolution of an ionizationâ€¦ (More)

We discuss a moving boundary problem modeling tumor growth in in vitro tissue cultures. It is shown that the unique flat steady state solution is exponentially stable with respect to generalâ€¦ (More)

We investigate a moving boundary problem with a gradient flow structure which generalizes Hele-Shaw flow driven solely by surface tension to the case of nonconstant surface tension coefficient takenâ€¦ (More)

In the free boundary problem of Stokes flow driven by surface tension, we pass to the limit of small layer thickness. It is rigorously shown that in this limit the evolution is given by theâ€¦ (More)

Let X,Y be normed spaces. The set of bounded linear operators is noted as L(X,Y ). Let now D = D(A) âŠ‚ X be a linear subspace, and A : D âˆ’â†’ Y a linear (not necessarily bounded!) operator. Notation:â€¦ (More)