The (Variable Coefficient) Thin Obstacle Problem: A Carleman Approach

In this talk I discuss a robust, new approach of proving (almost) optimal regularity for the (variable coefficient) thin obstacle problem. The central tool here consists of a Carleman inequality. This allows to control the vanishing order of solutions to the problem and to deduce compactness of blow-up solutions also in the presence of metrics with low regularity. This is joint work with Herbert Koch and Wenhui Shi.