$L^p$ Neumann Problems in Homogenization of General Elliptic Systems

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.

arXiv comment26 pages

References in corpus (5)

• An optimal error estimate in stochastic homogenization of discrete elliptic equations
• Convergence Rates in L^2 for Elliptic Homogenization Problems
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Cited by in corpus (1)

• Quantitative Estimates on Periodic Homogenization of Nonlinear Elliptic Operators