Optimal Regularity in the Thin Obstacle Problem with Lipschitz Variable Coefficients
Mariana Smit Vega Garcia, Purdue University
Location: Stevenson 1307
We will describe the lower-dimensional obstacle problem for a uniformly elliptic, divergence form operator $L = div(A(x)\nabla)$ with Lipschitz continuous coefficients and discuss the optimal regularity of the solution. Our main result states that, similarly to what happens when $L = \Delta$, the variational solution has the optimal interior regularity. We achieve this by proving some new monotonicity formulas for an appropriate generalization of Almgren's frequency functional. This is joint work with Nicola Garofalo.