Symmetry and Convexity of Level Sets of Solutions to the Infinity Laplace's Equation
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We consider the Dirichlet problem -Δ∞u = f(u) in Ω, u = 0 on ∂Ω, where Δ∞u = u(x)(i), u(x)(j), u(x)(i)(x)j) 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.