摘要
该文考虑光滑闭Jondan曲线Γ围成的单连区域D,证明了在Γ上具有已知导数数据的D内调和函数u(x,y)的存在性.继而构造了一个调和插值多项式序列在(?)=D∪Γ上一致收敛于u(x,y),且具理想的收敛速度.此外,以往同类研究工作中的边界Γ是解析曲线,而在该文中已减少边界限制为Γ∈J_0.
Suppose D is a simply connected domain bounded by a smooth closed Jordan curveΓ.In D the existence of a harmonic function u（x,y） with given derivative boundary data onΓis proved.By the way,the line integral representation of such a harmonic function u（x,y） is obtained.Moreover,the authors construct a sequence of harmonic interpolation polynomials uniformly convergent to u（x,y） on D^- =D∪Γwith the desirable rate of convergence.In addition,the boundary condition thatΓis an analytic curve in early similar works is decreased toΓ∈J0 in this paper.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2010年第2期397-404,共8页
Acta Mathematica Scientia
基金
河南省自然科学基金(974050900)资助
关键词
调和函数
导数边界数据
调和插值多项式
一致收敛
收敛速度
Harmonic function
Derivative boundary data
Harmonic interpolation polynomial
Uniform convergence
Rate of convergence
