The Discrete and Classical Dirichlet Problem: Part II

详细信息    查看全文

• 作者：Nicolas Th. Varopoulos
• 关键词：Primary 60G17 ; 60G15 ; Secondary 60G50 ; 31B25 ; 31B99 ; 42B25 ; 42B30 ; 42B35 ; Dirichlet Problem ; harmonic functions ; random walks ; finite differences ; Quasidiscs
• 刊名：Milan Journal of Mathematics
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：83
• 期：1
• 页码：1-20
• 全文大小：764 KB
• 参考文献：1.G. F. Lawler, Intersection of Random Walks. Birkh盲user, 1991.
  2.Jerison D., Kenig C.: Boundary behaviour of harmonic functions in nontangentially accessible domains. Advances in Math. 46, 80鈥?47 (1982)View Article MATH MathSciNet
  3.Chelkak D., Smirnov S.: Discrete complex analysis on isoradial graphs. Adv. Math 228, 1590鈥?630 (2011)View Article MATH MathSciNet
  4.B. V. Gnedenko, A. N. Kolmogorov, Limit distributions for sums of independent random variables. Addison-Wesley, 1954
  5.O. Lehto and K.I. Virtanen, Quasiconformal Mappings in the plane. Springer-Verlag, 1973.
  6.N.Th. Varopoulos, The discrete and classical Dirichlet problem, Milan J. Math. 77 (2009), 397鈥?36.
  7.N.Th. Varopoulos, The Central Limit Theorem in Lipschitz Domains (an overview and the conformal invariance), Math. Proc. Camb. Phil. Soc. 139 (2005), 161鈥?80.
  8.R. Courant, K. Friedrichs, H. Lewy, On the partial differential equations of mathematical physics, Math. Ann. 100 (1928), 32鈥?4
  9.L. Breiman, Probability. Addison-Wesley, 1968
  
• 作者单位：Nicolas Th. Varopoulos (1)
  
  1. 61, rue Raymond 鈥?Losserand, Paris, 75014, France
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1424-9294

文摘

For any domain \({\Omega \subset \mathbb{R}^{p}}\) , we denote by u the solution of the Dirichlet Problem with data f at the boundary. Similarly, we denote by u _d the solution that satisfies the average property on a discrete grid and the same boundary data. We give optimal estimates for the difference \({\|u-u_{d}\|_{\infty}}\) .