Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (2): 397-404.

• Articles • Previous Articles     Next Articles

Interpolatory Approximation to Harmonic Function with Boundary Data

TU Tian-Liang1, MO Jiong2   

  1. 1.Department of Mathematics and Informatics, North China Institute of Water Conservancy and Hydroelectric power, Zhengzhou 450011|2.Department |of Physics, Zhengzhou University, Zhengzhou 450052
  • Received:2006-04-11 Revised:2009-03-08 Online:2010-04-25 Published:2010-04-25
  • Supported by:

    河南省自然科学基金(974050900)资助.

Abstract:

Suppose D is a simply connected domain bounded by a smooth closed Jordan curve Γ. In D the existence of a  harmonic function u(x, y) with given derivative boundary data on Γ is 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 ∪ 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.

Key words: Harmonic function, Derivative boundary data,  Harmonic interpolation polynomial,  Uniform convergence, Rate of
convergence

CLC Number: 

  • 35E05
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