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中文摘要：
文中研究了Hamilton-Jacobi方程ut＋H（u,Du）=0,（p,t）∈G×（0,∞），这里G是Carnot群，Du表示u的水平梯度。当函数H（γ,x）对变量γ∈R^m是凸的、径向且一阶齐次时，建立了该方程在有界连续初值u（p,0）=g（p）下有界粘性解的存在唯一性，其解由Hopf-Lax公式给出u（p,t）=q∈G^min{h（t^——q^-1.p）∨g（q）},其中函数h是由函数H（γ,x）关于变量x∈R^m的拟凸对偶提升到G上的，且关于Carnot-Carathéodory距离是径向的。
英文摘要：
In this paper the author consider Hamilton-Jacobi equations ut＋H（u, Du） = 0 in the G× （0, ＋∞）, where G is Carnot group and Du denotes the horizontal gradient of u. When H（γ,x） is assumed to be nondecreasing in γ∈R and convex and radial andpositively homogeneous of degree 1 in x∈R^m, the uniqueness of bounded viscosity solutions is established with bounded continuous initial data u（p, O） = g（p）, the solution is given by the Hopf-Lax formula u（p,t）=q∈G^min{h（t^--q^-1.p）∨g（q）} where h is the quasiconvex dual of （γ,x） in x E Rm lifted to G by requiring it to be radial with respect to the Carnot-Carathéodory metric.
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