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標題: Discrete Mean Value Theorem
作者: 林郁翔
Yu-Siang Lin
引用: [1] Pei-Yu Chung, On Sharper Forms of the Discrete Theorem and Green's Identities in a Disk, theses of master degree, National Chung-Hsing University, 2007. [2] D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, 2nd edition, Springer Verlag, 1983. [3] Bi-Jin Huang, Some Discrete Green Identities on a Disk, theses of master degree, National Chung-Hsing University, 2005. [4] Yun-Wen Jin, Discrete Divergence Theorem and Green's Identities on a 3-ball, theses of master degree, National Chung-Hsing University, 2008. [5] Han-Chia Weng, Some properties of elliptic difference equations, National Chung-Hsing Uni- versity, 2013.
摘要: In this thesis, we derive the mean value theorems for the super-harmonic, sub-harmonic and harmonic solutions on square domains. Moreover, we consider the mesh functions on the mesh squares and establish the discrete mean value theorem by using the Green's identities on rectangles in R2. From the discrete mean value theorem, we obtain that the value of a discrete harmonic function at a mesh point (x0, y0) is the average of any discrete square which has center at this mesh point (x0, y0) . For further research, it is interesting to extend the result here to n-dimensional space.
首先我們導引上調和,下調和及調和函數在一正方形上的平均值定理。然後 我們利用離散型格林定理去建立離散型調和函數在離散正方形上的平均值,對未來的研究,本論文的結果應可考慮擴充到n-維度空間。
文章公開時間: 2018-07-27
Appears in Collections:應用數學系所



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