Symmetry and Convexity of Level Sets of Solutions to the Infinity Laplace’s Equation

We consider the Dirichlet problem −∆∞u = f(u) in Ω , u = 0 on ∂Ω , where ∆∞u = uxiuxjuxixj and f is a nonnegative continuous function. We investigate whether the solutions to this equation inherit geometrical properties from the domain Ω. We obtain results concerning convexity of level sets and symmetry of solutions.