The obstacle problem with singular coefficients near Dirichlet data

Let Γ=B+∩∂{u>0} be the free boundary and assume that the origin is a contact point, i.e. 0∈Γ‾. We prove that the free boundary touches the fixed boundary uniformly tangentially at the origin, near to the origin it is the graph of a C1 function and there is a uniform modulus of continuity for the derivatives of this function.