FRACTAL RELAXED DIRICHLET PROBLEMS

Given a self similar fractal K subset of IR(n) of Hausdorff dimension alpha > n - 2, and c(1) > 0, we give an easy and explicit construction , using the self similarity properties of K, of a sequence of closed s ets E(h) such that for every bounded open set Omega subset of IR(n) an d for every f epsilon L(2)(Omega) the solutions to [GRAPHICS] converge to the solution of the relaxed Dirichlet boundary value problem [GRAP HICS] (H-\ K(alpha) denotes the restriction of the alpha-dimensional H ausdorff measure to K). The condition alpha > n - 2 is strict.