<inline-formula><tex-math id="M1">\begin{document}$ L^p $\end{document}</tex-math></inline-formula> Neumann problems in homogenization of general elliptic operators

Abstract

In this paper, we extend the nontangential maximal function estimates in $ L^p $-norm obtained by C. Kenig, F. Lin and Z. Shen [13] to the nonhomogeneous elliptic operators with rapidly oscillating periodic coefficients. The result relies on a local Lipschitz boundary estimate, which has not been established in [29]. The present argument develops some new techniques to make the Campanato iteration and real methods workable for general elliptic operators. The result is new even for effective operators, as well as general elliptic equations of scalar.