Interests of reseach
My research interests cover several areas in partial differential equations and their applications.
My main results are in harmonic maps, elliptic-parabolic equations, mean curvature equations in phase change systems  and filtration flow.

Harmonic Maps
In harmonic maps my contribution is an interpolation lemma for boundary values which can be used to prove partial regularity results for minimizers of fairly general variational problems, say p-harmonic obstacle problems.

Elliptic-Parabolic Equations
In elliptic parabolic equations my results together with H. W. Alt on existence of weak solutions, later extended with A. Visintin to Stefan type systems, have been used widely in situations where the semigroup approach does not work.
Main applications are the equations of filtration flow and the already mentioned phase change systems.

Surface Tension in Phase Change Systems
The investigations of phase change systems with surface tension bring together my earlier interest in the mean curvature equation and the work on Stefan problems. Mathematically the main result is a capacity type estimate which allows to estimate oscillations in time of the phase in systems which lack time derivatives for these functions.

Filtration Flow
The investigations of filtration flow have lead on to work on periodic homogenization with singular scalings. In the work with Bourgeat and Mikelic a blow up (or periodic modulation) technique was introduced for such systems. This technique has been refined in a recent paper with Filo to show the relationship between uniqueness results for the blow up equation in the unbounded space and homogenization.

Current projects