Geodesic
Extending infinity harmonic functions by rotation
Electronic Journal of Differential Equations, Tome 2015 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $u(\mathbf{x},-y)=u(\mathbf{x},y))$.
Classification : 35J60, 35J70
Keywords: infinity harmonic, extension, viscosity solution 
@article{EJDE_2015__2015__a62,
     author = {Gripenberg, Gustaf},
     title = {Extending infinity harmonic functions by rotation},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a62/}
}
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Gripenberg, Gustaf. Extending infinity harmonic functions by rotation. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a62/