Geodesic
Boundary differentiability for inhomogeneous infinity Laplace equations
Electronic journal of differential equations, Tome 2014 (2014)
We study the boundary regularity of the solutions to inhomogeneous infinity Laplace equations. We prove that if $u\in C(\bar{\Omega})$ is a viscosity solution to $\Delta_{\infty}u:=\sum_{i,j=1}^n u_{x_i}u_{x_j}u_{x_ix_j}=f$ with $f\in C(\Omega)\cap L^{\infty}(\Omega)$ and for $x_0\in \partial\Omega$ both $\partial\Omega$ and $g:=u|_{\partial\Omega}$ are differentiable at $x_0$, then u is differentiable at $x_0$.
Classification : 35J25, 35J70, 49N60
Keywords: boundary regularity, infinity Laplacian, comparison principle, monotonicity 
@article{EJDE_2014__2014__a183,
     author = {Hong,  Guanghao},
     title = {Boundary differentiability for inhomogeneous infinity {Laplace} equations},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1291.35092},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a183/}
}
TY  - JOUR
AU  - Hong,  Guanghao
TI  - Boundary differentiability for inhomogeneous infinity Laplace equations
JO  - Electronic journal of differential equations
PY  - 2014
VL  - 2014
UR  - http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a183/
LA  - en
ID  - EJDE_2014__2014__a183
ER  - 
%0 Journal Article
%A Hong,  Guanghao
%T Boundary differentiability for inhomogeneous infinity Laplace equations
%J Electronic journal of differential equations
%D 2014
%V 2014
%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a183/
%G en
%F EJDE_2014__2014__a183
Hong,  Guanghao. Boundary differentiability for inhomogeneous infinity Laplace equations. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a183/