On the regularity of the non-dynamic parabolic fractional obstacle problem

In the class of the non-dynamic Fractional Obstacle Problems of parabolic type, it is shown existence, uniqueness, apriori bounds of the solution and optimal regularity of the space derivatives of the solution. Furthermore, at free boundary points of positive parabolic density, it is proven that the time derivative of the solution is Hölder continuous. At such free boundary points, space-time regularity of the corresponding free boundary is obtained for any fraction s∈(0,1).