论文标题
Carnot-Carathéodory空间中至上功能的绝对最小化器的Aronsson方程
The Aronsson Equation for Absolute Minimizers of Supremal Functionals in Carnot-Carathéodory Spaces
论文作者
论文摘要
Given a $C^2$ family of vector fields $X_1,...,X_m$ which induces a continuous Carnot-Carathéodory 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
Given a $C^2$ family of vector fields $X_1,...,X_m$ which induces a continuous Carnot-Carathéodory 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 $-\langle X(f(x, u(x), Xu(x))), D_p f(x, u(x), Xu(x))\rangle = 0.$
