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|標題:||Discrete Mean Value Theorem|
|引用:|| 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.  D. Gilbarg and N. S. Trudinger, Elliptic partial diﬀerential equations of second order, 2nd edition, Springer Verlag, 1983.  Bi-Jin Huang, Some Discrete Green Identities on a Disk, theses of master degree, National Chung-Hsing University, 2005.  Yun-Wen Jin, Discrete Divergence Theorem and Green's Identities on a 3-ball, theses of master degree, National Chung-Hsing University, 2008.  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
|Appears in Collections:||應用數學系所|
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