Distance boundary condition domains and Hlder continuity;

This paper discusses Hlder continuity for minimum of free discontinuity prob- lems,namely we prove that the function is Hlder continuous out of a neighborhood of the singular set.

Under the hypothesis that the first order derivative of a nonlinear operator f satisfied Hlder continuous condition around the zero of f(x),a local convergence theorem for this method was established in Banach spaces,and the local convergence with order 1+p was presented.