Given a C-2 family of vector fields X-1, ... , X-m which induces a continuous Carnot-Caratheodory distance, we show that any absolute minimizer of a supremal functional defined by a C-2 quasiconvex Hamiltonian f (x, s, P), allowing s-variable dependence, is a viscosity solution to the Aronsson equation-Sigma(m)(i=1) X-i(f (x, u(x), Xu(x))) partial derivative f/partial derivative Pi (x, u(x), Xu(x)) = 0,
The Aronsson equation for absolute minimizers of supremal functionals in Carnot–Carathéodory spaces
Verzellesi S.;
2023
Abstract
Given a C-2 family of vector fields X-1, ... , X-m which induces a continuous Carnot-Caratheodory distance, we show that any absolute minimizer of a supremal functional defined by a C-2 quasiconvex Hamiltonian f (x, s, P), allowing s-variable dependence, is a viscosity solution to the Aronsson equation-Sigma(m)(i=1) X-i(f (x, u(x), Xu(x))) partial derivative f/partial derivative Pi (x, u(x), Xu(x)) = 0,
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