Electron. J. Diff. Equ., Vol. 2014 (2014), No. 72, pp. 1-6.

Boundary differentiability for inhomogeneous infinity Laplace equations

Guanghao Hong

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.

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Guanghao Hong
School of Mathematics and Statistics
Xi'an Jiaotong University
Xi'an, 710049, China
email: ghhongmath@gmail.com

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