Tomohiko Sato, Takashi Suzuki, Futoshi Takahashi
Abstract:
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 Gakushuin University 1-5-1 Mejiro, Toshima-ku, Tokyo, 171-8588, Japan email: tomohiko.sato@gakushuin.ac.jp | |
Takashi Suzuki Division of Mathematical Science, Department of System Innovation Graduate School of Engineering Science, Osaka University Machikaneyamacho 1-3, Toyonakashi, 560-8531, Japan email: suzuki@sigmath.es.osaka-u.ac.jp | |
Futoshi Takahashi Department of Mathematics, Graduate School of Science Osaka City University Sugimoto 3-3-138, Sumiyoshiku, Osakashi, 535-8585, Japan email: futoshi@sci.osaka-cu.ac.jp |
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