Electron. J. Diff. Equ., Vol. 2015 (2015), No. 149, pp. 1-6.

Extending infinity harmonic functions by rotation

Gustaf Gripenberg

Abstract:
If $u(\mathbf{x}, y)$ is an infinity harmonic function, i.e., a viscosity solution to the equation $-\Delta_\infty u=0$ in $\Omega \subset \mathbb{R}^{m+1}$ then the function $v(\mathbf{x}, \mathbf{z})= u(\mathbf{x}, \|\mathbf{z}\|)$ is infinity harmonic in the set $\{(\mathbf{x}, \mathbf{z}): (\mathbf{x}, \|\mathbf{z}\|)\in \Omega\}$ (provided $u(\mathbf{x},-y)=u(\mathbf{x},y)$).

Submitted May 21, 2015. Published June 10, 2015.
Math Subject Classifications: 35J60, 35J70.
Key Words: Infinity harmonic; extension; viscosity solution.

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Gustaf Gripenberg
Department of Mathematics and Systems Analysis
Aalto University
P.O. Box 11100, FI-00076 Aalto, Finland
email: gustaf.gripenberg@aalto.fi

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