Wenhui Shi: Higher regularity of the free boundary in the thin obstacle problem

I will describe how to use the partial hodograph-Legendre transformation to show the analyticity of the free boundary in the thin obstacle problem.

In particular, I will discuss the invertibility of this transformation and show that the resulting fully nonlinear PDE has a subelliptic structure. This is based on a joint work with Herbert Koch and Arshak Petrosyan.