A two-phase obstacle-type problem for the p-Laplacian

We study the so-called two-phase obstacle-type problem for the p-Laplacian when p is close to 2. We introduce a new method to obtain the optimal growth of the function from branch points, i.e. two-phase points in the free boundary where the gradient vanishes. As a by-product we can locally estimate the (n − 1)-Hausdorff-measure of the free boundary for the special case when p > 2. This research project is a part of the ESF program Global. E. Lindgren has been supported by grant KAW 2005.0098 from the Knut and Alice Wallenberg foundation.