Convergence for elliptic equations in periodic perforated domains

Li-Ming Yeh*

*此作品的通信作者

研究成果: Article同行評審

1 引文 斯高帕斯(Scopus)

摘要

Convergence for the solutions of elliptic equations in periodic perforated domains is concerned. Let ε 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 ε in L2 space. Also, when ε approaches 0, the elliptic solutions converge to a solution of some simple homogenized elliptic equation. In this work, above results are extended to general W1,p space for p>1. More precisely, a uniform W1,p estimate in ε for p∈(1, ∞] and a W1,p convergence result for p∈(nn-2,∞] for the elliptic solutions in periodic perforated domains are derived. Here n is the dimension of the space domain. One also notes that the Lp norm of the second order derivatives of the elliptic solutions in general cannot be bounded uniformly in ε.

原文English
頁(從 - 到)1734-1783
頁數50
期刊Journal of Differential Equations
255
發行號7
DOIs
出版狀態Published - 1 10月 2013

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