The Aronsson Equation for Absolute Minimizers of Supremal Functionals in Carnot-Carath\'eodory Spaces
Abstract
Given a C2 family of vector fields X1,...,Xm which induces a continuous Carnot-Carath\'eodory distance, we show that any absolute minimizer of a supremal functional defined by a C2 quasiconvex Hamiltonian f(x, z, p), allowing z-variable dependence, is a viscosity solution to the Aronsson equation - X(f(x, u(x), Xu(x))), Dp f(x, u(x), Xu(x)) = 0.
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