Lp gradient estimate for elliptic equations with high-contrast conductivities in Rn

Li-Ming Yeh*

*Corresponding author for this work

研究成果: Article同行評審

2 引文 斯高帕斯(Scopus)

摘要

Uniform estimate for the solutions of elliptic equations with high-contrast conductivities in Rn is concerned. The space domain consists of a periodic connected sub-region and a periodic disconnected matrix block subset. The elliptic equations have fast diffusion in the connected sub-region and slow diffusion in the disconnected subset. Suppose ε∈(0, 1] is the diameter of each matrix block and ω2∈(0, 1] is the conductivity ratio of the disconnected matrix block subset to the connected sub-region. It is proved that the W1,p norm of the elliptic solutions in the connected sub-region is bounded uniformly in ε, ω when ε≤ω, the Lp norm of the elliptic solutions in the whole space is bounded uniformly in ε, ω the W1,p norm of the elliptic solutions in perforated domains is bounded uniformly in ε. However, the Lp norm of the second order derivatives of the solutions in the connected sub-region may not be bounded uniformly in ε, ω.

原文English
頁(從 - 到)925-966
頁數42
期刊Journal of Differential Equations
261
發行號2
DOIs
出版狀態Published - 15 七月 2016

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