Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 34, pp. 1-12.
Title: Symmetry and convexity of level sets of solutions to
infinity Laplace's equation
Author: Edi Rosset (Univ. degli Studi di Trieste, Italy)
Abstract:
We consider the Dirichlet problem
$$\displaylines{
-\Delta_\infty u=f(u) \quad \hbox{in }\Omega\,,\cr
u=0\quad \hbox{on }\partial\Omega\,,}
$$
where $\Delta_\infty u=u_{x_i}u_{x_j}u_{x_ix_j}$ and
$f$ is a nonnegative continuous function.
We investigate whether the solutions to this equation
inherit geometrical properties from the domain $\Omega$.
We obtain results concerning convexity of level sets
and symmetry of solutions.
Submitted July 23, 1998. Published December 9, 1998.
Math Subject Classification: 35J70, 35B05.
Key Words: Infinity-Laplace equation; p-Laplace equation.