The Aronsson Equation for Absolute Minimizers of Supremal Functionals in Carnot-Carath\'eodory Spaces
| Autor: | Pinamonti, Andrea, Verzellesi, Simone, Wang, Changyou |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Given a $C^2$ family of vector fields $X_1,...,X_m$ 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 $-\langle X(f(x, u(x), Xu(x))), D_p f(x, u(x), Xu(x))\rangle = 0.$ |
| Databáze: | arXiv |
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