数学物理学报
數學物理學報
수학물이학보
ACTA MATHEMATICA SCIENTIA
2010年
2期
397-404
,共8页
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
調和函數%導數邊界數據%調和插值多項式%一緻收斂%收斂速度
조화함수%도수변계수거%조화삽치다항식%일치수렴%수렴속도
Harmonic function%Derivative boundary data%Harmonic interpolation polyno-mial%Uniform convergence%Rate of convergence
该文考虑光滑闭 Jondan曲线г围成的单连区域D,证明了在г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)=D U 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г是解析曲线,而在该文中已减少边界限制为г∈J0.
該文攷慮光滑閉 Jondan麯線г圍成的單連區域D,證明瞭在г上具有已知導數數據的D內調和函數u(x,y,)的存在性.繼而構造瞭一箇調和插值多項式序列在(D)=D U Γ上一緻收斂于u(x,y),且具理想的收斂速度.此外,以往同類研究工作中的邊界г是解析麯線,而在該文中已減少邊界限製為г∈J0.
해문고필광활폐 Jondan곡선г위성적단련구역D,증명료재г상구유이지도수수거적D내조화함수u(x,y,)적존재성.계이구조료일개조화삽치다항식서렬재(D)=D U Γ상일치수렴우u(x,y),차구이상적수렴속도.차외,이왕동류연구공작중적변계г시해석곡선,이재해문중이감소변계한제위г∈J0.
Suppose D is a simply connected domain bounded by a smooth closed Jordan curve obtained. Moreover, the authors construct a sequence of harmonic interpolation polynomials uniformly convergent to u(x,y) on (D)=D U Γ with the desirable rate of convergence.In addition,the boundary condition that Γ is an analytic curve in early similar works is decreased to Γ ∈J0 in this paper.
