The obstacle problem for elliptic and parabolic equations is a
topics which attracted a great interest in the past years. However,
even if many studies are available on second order elliptic and
parabolic equations, there are relatively few results for higher
order obstacle problem, even in the linear fourth order case.

In this talk, we show a recent joint work with M. Novaga (Pisa
University) on the obstacle problem for the parabolic biharmonic
equation. We analyze the problem via an implicit time discretization,
and we prove an existence of the solution and its regularity properties.
Since our motivation for the obstacle problem rose from a geometric
obstacle problem, we wish to mention the geometric obstacle problem.