## Differential and Integral Equations

### Stability for the infinity-laplace equation with variable exponent

#### Abstract

We study the stability for the viscosity solutions of the differential equation $$\sum u_{x_i}u_{x_j}u_{x_i x_j}+ | {\nabla u} | ^2\ln( | {\nabla u} | )\langle\nabla u, \nabla \ln p \rangle=0$$ under perturbations of the function $p(x).$ The differential operator is the so-called $\infty(x)$-Laplacian.

#### Article information

Source
Differential Integral Equations, Volume 25, Number 5/6 (2012), 589-600.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356012682

Mathematical Reviews number (MathSciNet)
MR2951744

Zentralblatt MATH identifier
1265.35105

Subjects
Primary: 35J70: Degenerate elliptic equations 49K35: Minimax problems

#### Citation

Lindgren, Erik; Lindqvist, Peter. Stability for the infinity-laplace equation with variable exponent. Differential Integral Equations 25 (2012), no. 5/6, 589--600. https://projecteuclid.org/euclid.die/1356012682