PARTIAL REGULARITY FOR WEAK SOLUTIONS OF ANISOTROPIC LANE-EMDEN EQUATION

We study positive weak solutions of the quasilinear Lane-Emden equation -Qu = u(alpha) in Omega subset of R-n, where alpha >= n+2/n-2, for n >= 3, is supercritical and the operator Q, known as Finsler-Laplacian or anisotropic Laplacian, is defined by Qu := Sigma(n)(i=1)partial derivative/partial derivative x(i)(F(del u)F-xi i(del u)). Here, F-xi i = partial derivative F/partial derivative xi(i) and F : R-n -> [0, +infinity) is a convex function of C-2(R-n\{0}), that satisfies positive homogeneity of first order and other certain assumptions. We prove that the Hausdorff dimension of singular set of u is less than n-2 alpha+1/alpha-1.