REGULARITY FOR MINIMAL BOUNDARIES IN R-N WITH MEAN-CURVATURE IN L-N

Let E(0)subset of or equal to R-n be a minimal set with mean curvature in L-n that is a minimum of the functional E bar right arrow P(E, Ome ga) + integral(E boolean AND Omega) H, where Omega subset of or equal to R-n is open and H is an element of L-n(Omega). We prove that if 2 l ess than or equal to n less than or equal to 7 then partial derivative E-0 can be parametrized over the (n - 1)-dimensional disk with a C-0, C-alpha mapping with C-0,C-alpha inverse.