Electron. J. Diff. Equ., Vol. 2014 (2014), No. 109, pp. 1-17.

Existence of solutions to a normalized F-infinity Laplacian equation

Hua Wang, Yijun He

Abstract:
In this article, for a continuous function F that is twice differentiable at a point $x_0$, we define the normalized F-infinity Laplacian $\Delta_{F; \infty}^N$ which is a generalization of the usual normalized infinity Laplacian. Then for a bounded domain $\Omega\subset\mathbb{R}^n$, $f\in C(\Omega)$ with $\inf_\Omega f(x)>0$ and $g\in C(\partial\Omega)$, we obtain existence and uniqueness of viscosity solutions to the Dirichlet boundary-value problem
$$\displaylines{ \Delta_{F; \infty}^N u=f, \quad \text{in }\Omega,\cr u=g, \quad \text{on }\partial\Omega. }$$

Submitted March 18, 2014. Published April 16, 2104.
Math Subject Classifications: 35D40, 35J60, 35J70
Key Words: March 18, 2014. Published April 16, 2014.

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Hua Wang
School of Mathematical Sciences, Shanxi University
Taiyuan 030006, China
email: 197wang@163.com
Yijun He
School of Mathematical Sciences, Shanxi University
Taiyuan 030006, China
email: heyijun@sxu.edu.cn

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