E^n子区域里函数的连续延拓及调和性

Continual Extension and Harmony of Function in E^n's Smaller Area

讨论在给出En 的子区域里函数是否连续延拓并具有调和性 ,给出一个函数u在一点P∈En的一个邻域里若有定义 ,且满足一定条件 ,则u在P点调和 ,并推出函数在一个点集中点点调和及在点集中调和直至推出函数在En 子区域里调和 ;假定函数 f在一个球面S(P0 ,R)上连续 ,则u(Q)在一定条件下关于Q∈K(P0 ,R)调和 ,且可以用f(P)连续延拓到S(P0 ,R)上去 ,探讨了En 上的Radon测度 μ在一点P0 ∈En 的一个邻域V上满足一定条件则有位势在P0

The paper is intended to discuss whether Function in E n 's son area has a continual extension and harmony,giving Function u is in harmony with Point P if a Point P∈E n has a definition in a neighbouring area, satisfied with a certain condition and proving that function certers on a point,harmonizes every point,focuses on harmonizing on the point and turns out the harmony with its function in E n 's son area.If Function f continues on a spherical surface S(P 0,R) , u(Q) is in harmony with Q∈K(P 0,R) under a certain condition, and f(P) extends on S(P 0,R). The article probes on E n Radon measure μ rests content with a certain condition on a Point P 0∈E n 's neighbouring area V and has the potentiality of Upper Harmony and low one on P 0 .The conclusion is that Function in E n 's son area can be continually extended and harmonized.