Partial regularity for weak solutions of semilinear elliptic equations with supercritical exponents

Zongming Guo and Jiayu Li

Vol. 214 (2004), No. 1, 89–107

DOI: 10.2140/pjm.2004.214.89

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 ∈ 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.

Milestones

Received: 30 January 2001

Revised: 24 June 2002

Published: 1 March 2004