Geodesic
Extending infinity harmonic functions by rotation
Electronic journal of differential equations, Tome 2015 (2015)
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},
     year = {2015},
     volume = {2015},
     zbl = {1320.31015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a62/}
}
TY  - JOUR
AU  - Gripenberg,  Gustaf
TI  - Extending infinity harmonic functions by rotation
JO  - Electronic journal of differential equations
PY  - 2015
VL  - 2015
UR  - http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a62/
LA  - en
ID  - EJDE_2015__2015__a62
ER  - 
%0 Journal Article
%A Gripenberg,  Gustaf
%T Extending infinity harmonic functions by rotation
%J Electronic journal of differential equations
%D 2015
%V 2015
%U http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a62/
%G en
%F EJDE_2015__2015__a62
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/