$L^p$ Neumann Problems in Homogenization of General Elliptic Systems
Analysis of PDEs
2018-06-08 v1
Abstract
In this paper, we extend the nontangential maximal function estimate obtained by C. Kenig, F. Lin and Z. Shen in \cite{KFS1} to the nonhomogeneous elliptic operators with rapidly oscillating periodic coefficients. The result relies on the previous work \cite{X2}, and optimal boundary estimates which is based upon certain estimates on convergence rates. Compared to the homogeneous case, the additional bootstrap process seems inevitable, and the Neumann boundary corrector caused by the lower order term are still useful here.
Keywords
Cite
@article{arxiv.1806.02632,
title = {$L^p$ Neumann Problems in Homogenization of General Elliptic Systems},
author = {Qiang Xu and Shulin Zhou},
journal= {arXiv preprint arXiv:1806.02632},
year = {2018}
}
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26 pages