Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 72, pp. 1-6.

Title: Boundary differentiability for inhomogeneous infinity Laplace equations

Author: Guanghao Hong (Xi'an Jiaotong Univ., Xi'an, China)

Abstract:
 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 $x_0$.

Submitted December 17, 2013. Published March 16, 2014.
Math Subject Classifications: 35J25, 35J70, 49N60.
Key Words: Boundary regularity; infinity Laplacian; comparison principle;
           monotonicity.