海森堡型群上Hamilton-Jacobi方程的粘性解

The viscosity solutions of Hamilton-Jacobi equations in groups of Heisenberg type

研究了G×R+上的Hamilton-Jacobi方程ut+H(Du)=0,这里G表示海森堡型群,Du表示u的水平梯度,当H是径向的、凸的、超线性的时,建立了在连续初值u(p,0)=g(p)条件下有界粘性解的唯一性。

Hamilton-Jacobi equationsu_t+H(Du)=0 in G×R^+was considered, where G is a group of Heisenberg type and Du denotes the horizontal gradient of u.When H is radial, convex and superlinear,the uniqueness of bounded viscosity solutions with continuous initial data u(p,0)=g(p) was established.