標題: | L-p gradient estimate for elliptic equations with high-contrast conductivities in R-n |
作者: | Yeh, Li-Ming 應用數學系 Department of Applied Mathematics |
關鍵字: | High-contrast conductivity;Potentials;Duality argument;Embedding theory |
公開日期: | 15-七月-2016 |
摘要: | Uniform estimate for the solutions of elliptic equations with high-contrast conductivities R-n 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 epsilon is an element of (0, 1] is the diameter of each matrix block and omega(2) is an element of a (0, 1] is the conductivity ratio of the disconnected matrix block subset to the connected sub-region. It is proved that the W-1,W-p norm of the elliptic solutions in the connected sub-region is bounded uniformly in epsilon, is an element of, on when epsilon <= is an element of, the L-p norm of the elliptic solutions in the whole space is bounded uniformly in epsilon, omega; the W-1,W-p norm of the elliptic solutions in perforated domains is bounded uniformly in epsilon. However, the L-p norm of the second order derivatives of the solutions in the connected sub-region may not be bounded uniformly in epsilon, omega. (C) 2016 Elsevier Inc. All rights reserved. |
URI: | http://dx.doi.org/10.1016/j.jde.2016.03.027 http://hdl.handle.net/11536/133721 |
ISSN: | 0022-0396 |
DOI: | 10.1016/j.jde.2016.03.027 |
期刊: | JOURNAL OF DIFFERENTIAL EQUATIONS |
Volume: | 261 |
Issue: | 2 |
起始頁: | 925 |
結束頁: | 966 |
顯示於類別: | 期刊論文 |