Geodesic
Vanishing \(p\)-capacity of singular sets for \(p\)-harmonic functions
Electronic journal of differential equations, Tome 2011 (2011)
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.
Classification : 35B05, 35B45, 35J15, 35J70
Keywords: p-harmonic function, capacity, singular set, removable singularity, weak Sobolev space 
@article{EJDE_2011__2011__a38,
     author = {Sato,  Tomohiko and Suzuki,  Takashi and Takahashi,  Futoshi},
     title = {Vanishing \(p\)-capacity of singular sets for \(p\)-harmonic functions},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1254.35093},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a38/}
}
TY  - JOUR
AU  - Sato,  Tomohiko
AU  - Suzuki,  Takashi
AU  - Takahashi,  Futoshi
TI  - Vanishing \(p\)-capacity of singular sets for \(p\)-harmonic functions
JO  - Electronic journal of differential equations
PY  - 2011
VL  - 2011
UR  - http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a38/
LA  - en
ID  - EJDE_2011__2011__a38
ER  - 
%0 Journal Article
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%A Suzuki,  Takashi
%A Takahashi,  Futoshi
%T Vanishing \(p\)-capacity of singular sets for \(p\)-harmonic functions
%J Electronic journal of differential equations
%D 2011
%V 2011
%U http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a38/
%G en
%F EJDE_2011__2011__a38
Sato,  Tomohiko; Suzuki,  Takashi; Takahashi,  Futoshi. Vanishing \(p\)-capacity of singular sets for \(p\)-harmonic functions. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a38/