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