PARTIAL REGULARITY FOR WEAK SOLUTIONS OF A NONLINEAR ELLIPTIC EQUATION

For scalar non-linear elliptic equations, stationary solutions are def ined to be critical points of a functional with respect to the variati ons of the domain. We consider u a weak positive solution of -DELTAu = u(alpha) in OMEGA subset-of R(n), which is stationary. We prove that the Hausdorff dimension of the singular set of u is less than n-2alpha -1/alpha+1, if alpha greater-than-or-equal-to n-2/n+2.