Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 125, pp. 1-6.

Title: On Pacard's regularity for the equation $-\Delta u = u^p$
  
Author: David R. Adams (Univ. of kentucky, Lexington, KY, USA)

Abstract:
 It is shown that the singular set for a positive solution of
 the PDE  $-\Delta u = u^p$ has Hausdorff dimension 
 less than or equal to  $n - 2p'$, as conjectured by Pacard [12
 in 1993.

Submitted June 4, 2012. Published August 02, 2012.
Math Subject Classifications: 35D10, 35J60.
Key Words: Weak solutions; singular set; regularity.