Symmetry and Convexity of Level Sets of Solutions to the Infinity Laplace's Equation
MetadataShow full metadata
We consider the Dirichlet problem
-Δ∞u = ƒ(u) in Ω,
u = 0 on ∂Ω,
where Δ∞u = uxi, uxj, uxi xj and ƒ 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.
This work is licensed under a Creative Commons Attribution 4.0 International License.