Tomohiko Sato, Takashi Suzuki, Futoshi Takahashi
In this article, we study a counterpart of the removable singularity property of -harmonic functions. It is shown that p-capacity of the singular set of any -harmonic function vanishes, and such function is always weakly -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.
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| Tomohiko Sato |
Department of Mathematics, Faculty of Science
1-5-1 Mejiro, Toshima-ku, Tokyo, 171-8588, Japan
| Takashi Suzuki |
Division of Mathematical Science, Department of System Innovation
Graduate School of Engineering Science, Osaka University
Machikaneyamacho 1-3, Toyonakashi, 560-8531, Japan
| Futoshi Takahashi |
Department of Mathematics, Graduate School of Science
Osaka City University
Sugimoto 3-3-138, Sumiyoshiku, Osakashi, 535-8585, Japan
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