A symmetry problem in the calculus of variations

Let Omega be a ball in R(N), centered at zero, and let u be a minimizer of the nonconvex functional R(nu) = integral(Omega)1/1 + \del upsilon(x)\(2)dx over one of the classes C-M := {w is an element of W-loc(1,infinity) (Omega)\ 0 less than or equal to w(x) less than or equal to M in Omega, w concave} or E(M) := {w is an element of W-loc(1,2) (Omega) \0 less than or equal to w(x) less than or equal to M in Omega, Delta w less than or equal to 0 in L(1)(Omega)} of admissible functions. Then u is not radial and not unique, Therefore one can further reduce the resistance of Newton's rotational ''body of minimal resistance'' through symmetry breaking.