Electron. J. Diff. Eqns., Vol. 1994(1994), No. 09, pp. 1-4.

A Rado type theorem for p-harmonic functions in the plane

Tero Kilpelainen

Abstract:
We show that if $u\in C^1(\Omega)$ satisfies the p-Laplace equation
$$ {\rm div}(|\nabla u|^{p-2}\nabla u)=0 $$
in $\Omega\setminus \{x\ :u(x)=0\}$, then u is a solution to the p-Laplacian in the whole $\Omega\subset R^2$.

Submitted September 29, 1994.Published December 6, 1994.
Math Subject Classification: 35J60, 35B60, 31C45, 30C62.
Key Words: p-harmonic functions, p-Laplacian, removable sets.

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Tero Kilpelainen
Department of Mathematics, University of Jyvaskyla, P.O. Box 35, 40351 Jyvaskyla, Finland
e-mail: TeroK@math.jyu.fi
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