The Aronsson Equation for Absolute Minimizers of Supremal Functionals in Carnot-Carathéodory Spaces

created by pinamonti on 28 Feb 2022

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Inserted: 28 feb 2022
Last Updated: 28 feb 2022

Year: 2022

Abstract:

Given a $C^2$ family of vector fields $X_1,\ldots,X_m$ which induces a continuous Carnot-Carath\'eodory distance, we show that any absolute minimizer of a supremal functional defined by a $C^2$ quasiconvex Hamiltonian $f(x,z,p)$, allowing $z$-variable dependence, is a viscosity solution to the Aronsson equation $-\langle X(f(x,u(x),Xu(x))), D_pf(x,u(x),Xu(x))\rangle=0$