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A note on the Schwarz reflection principle for polyharmonic functions
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Dawit Aberra
Published/Copyright:
August 2, 2011
Abstract
In 1907, E. Study gave a geometric proof of the classical Schwarz reflection principle for harmonic functions. We show that this method can also be used to obtain the more general point-to-point reflection formula for polyharmonic functions in ℝ2. The advantage of this method over others is that it avoids use of Garabedian´s generalized Green´s functions.
Published Online: 2011-08-02
Published in Print: 2011-08
© by Oldenbourg Wissenschaftsverlag, Fort Valley, GA-31030, Germany
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Articles in the same Issue
- A note on the Schwarz reflection principle for polyharmonic functions
- Double series expression for the Stieltjes constants
- On the existence of normal Coulomb frames for two-dimensional immersions with higher codimension
- Traveling wave analysis for a mathematical model of malignant tumor invasion
- Exotic fractional part integrals and Euler´s constant
- A universal Cauchy–Riemann function on subsets of ℂn × ℝm
- Singular integrals associated with functions of finite type and extrapolation
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