A numerical finding of a 2D surface by its mean curvature

We consider the problem of finding of 2D surface Γ with a given mean curvature H in a small neighborhood of the given smooth surface Γ0 with mean curvature H0. The successive approximation method of finding Γ is based on the Lp-theory for the elliptic equations. It is assumed that p > 2 and Lp-norm of H-H0 is sufficiently small. This method is realized numerically for H0 = 0.