Electron. J. Diff. Equ., Vol. 2012 (2012), No. 125, pp. 1-6.

On Pacard's regularity for the equation $-\Delta u = u^p$

David R. Adams

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 2, 2012.
Math Subject Classifications: 35D10, 35J60.
Key Words: Weak solutions; singular set; regularity.

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David R. Adams
Department of Mathematics
University of kentucky, POT 714
Lexington, KY 40506, USA
email: dave@ms.uky.edu

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