摘要
设D是可求长Jordan闭曲线围成的单连域,g1(x,y)和g2(x,y)是D=Γ上的连续函数,证明了在D内调和且其连续偏导数可延拓到D=Γ上的调和函数存在的充要条件,讨论了这类边值问题解的惟一性,并得到了解的线积分表达式.
Let D be a simply connected domain bounded by a closed Jordan Curve F. Suppose g1 （x,y） and g2 （x,y） are continuous functions on F. The necessary and sufficient conditions for existence of u（x,y） are proved,which is harmonic in D and its continuous partial derivatives extending to δD ∈Г. The uniqueness of solution to the boundary value problem is discussed, and the representation of the solution is obtained.
出处
《华北水利水电学院学报》
2008年第4期100-101,共2页
North China Institute of Water Conservancy and Hydroelectric Power
关键词
边值问题
调和函数
存在性
惟一性
线积分表示
boundary value problem
harmonic function
existence uniqueness representation
