海森堡型群上粘性解的存在性和唯一性

Existence and uniqueness of viscosity solutions in groups of the Heisenberg type

研究了海森堡型群G上方程H(p,u(p),Du(p))=0,p∈G有界粘性解的存在性和唯一性理论．存在性的证明用Perron方法来完成,针对一特殊方程给出了粘性解的唯一性,这里日:G×R×Rm→R满足适当的条件,Du表示u在海森堡型群意义下的水平梯度．

In this paper the existence and uniqueness of bounded viscosity solutions of equution H（p, u（p）, Du（p）） = 0 on groups of Heisenberg type G are studied. Existence is proved by the Perron＇s method and, to a special equation, uniqueness is proved. Where H ： G ×]R × R^m→R satisfies certain conditions, Du denotes the horizontal gradient of u on groups in terms of Heisenberg type.