Electron. J. Diff. Eqns., Vol. 1998(1998), No. 34, pp. 1-12.

Symmetry and convexity of level sets of solutions to infinity Laplace's equation

Edi Rosset

We consider the Dirichlet problem
$-\Delta_\infty u=f(u)$ in $\Omega$, $u=0$ 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.

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Edi Rosset
Dipartimento di Scienze Matematiche
Universita degli Studi di Trieste
34100 Trieste, Italy
e-mail: rossedi@univ.trieste.it

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