Abstract

Let Ω be an open subset in Rⁿ (n ≥ 3). In this paper, we study the partial regularity for stationary positive weak solutions of the equation

We prove that if α > , and u in H¹(Ω) ∩ L^α+1(Ω) is a stationary positive weak solution of (1.1), then the Hausdorff dimension of the singular set of u is less than n − 2, which generalizes the main results in Pacard 1993 and Pacard 1994.

Authors