標題: Convergence for elliptic equations in periodic perforated domains
作者: Yeh, Li-Ming
應用數學系
Department of Applied Mathematics
關鍵字: Periodic perforated domain;Homogenized elliptic equation
公開日期: 1-十月-2013
摘要: Convergence for the solutions of elliptic equations in periodic perforated domains is concerned. Let epsilon denote the size ratio of the holes of a periodic perforated domain to the whole domain. It is known that, by energy method, the gradient of the solutions of elliptic equations is bounded uniformly in epsilon in L-2 space. Also, when epsilon approaches 0, the elliptic solutions converge to a solution of some simple homogenized elliptic equation. In this work, above results are extended to general W-1,W-p space for p > 1. More precisely, a uniform W-1,W-p estimate in epsilon for p is an element of (1, infinity] and a W-1,W-p convergence result for p is an element of (n/n-2, infinity] for the elliptic solutions in periodic perforated domains are derived. Here n is the dimension of the space domain. One also notes that the L-p norm of the second order derivatives of the elliptic solutions in general cannot be bounded uniformly in epsilon. (c) 2013 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.jde.2013.05.023
http://hdl.handle.net/11536/22090
ISSN: 0022-0396
DOI: 10.1016/j.jde.2013.05.023
期刊: JOURNAL OF DIFFERENTIAL EQUATIONS
Volume: 255
Issue: 7
起始頁: 1734
結束頁: 1783
顯示於類別:期刊論文


文件中的檔案:

  1. 000322092900014.pdf