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.
CitationRosset, E. (1998). Symmetry and convexity of level sets of solutions to the infinity Laplace's equation. Electronic Journal of Differential Equations, 1998,(34), pp. 1-12.
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