Generalized Cone Comparison Principle for Viscosity Solutions of the Aronsson Equation and Absolute Minimizers

Abstract

For any non-negative, quasi-convex Hamiltonian H ∈ C 2(R n ), we consider the L ∞-functional F(u, ·) = ‖H(∇ u)‖ L ∞(·) over . We introduce the notion of comparison with generalized cones (abbreviated CGC) and prove that CGC, viscosity solutions of the Aronsson equation, and absolute minimizers of F(·) are equivalent. This extends an earlier result by Crandall et al. (2001).