Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 67, pp. 1-15.

Title: Vanishing p-capacity of singular sets for p-harmonic functions
       
Authors: Tomohiko Sato (Gakushuin Univ., Tokyo, Japan)
         Takashi Suzuki (Osaka Univ., Toyonakashi, Japan)
         Futoshi TakahashiA (Osaka City Univ., Osakashi, Japan)

Abstract: 
 In this article, we study a counterpart of the removable
 singularity property of $p$-harmonic functions.
 It is shown that p-capacity of the singular set of any
 $p$-harmonic function vanishes, and such function is always
 weakly $N(p-1)/(N-p)$-integrable. Several related results
 are also shown.

Submitted April 4, 2011. Published May 18, 2011.
Math Subject Classifications: 35B05, 35B45, 35J15, 35J70.
Key Words: p-harmonic function; capacity; singular set;
           removable singularity; weak Sobolev space.