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

### Summary

Summary: 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.

35J70, 35B05

### Keywords/Phrases

infinity-Laplace equation, p-Laplace equation