| We study the interior Signorini, or lower-dimensional obstacle problem for a uniformly elliptic divergence form operator L = div( A(x)∇) with Lipschitz continuous coefficients.;Our main result states that, similarly to what happens when L = Delta, the variational solution has the optimal interior regularity C1,1/2loc(O +/- ∪ M), when M is a codimension one flat manifold which supports the obstacle. We achieve this by proving some new monotonicity formulas for an appropriate generalization of the celebrated Almgren's frequency functional. |
