Homogenization of Elliptic Boundary Value Problems in Lipschitz Domains

Details Homogenization of Elliptic Boundary Value Problems in Lipschitz Domains Homogenization of Elliptic Boundary Value Problems in Lipschitz Domains

2009-08-14

arxiv.org/abs/0908.2135v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper we study the $L^p$ boundary value problems for $\mathcal{L}(u)=0$ in $\mathbb{R}^{d+1}_+$, where $\mathcal{L}=-\text{div}(A\nabla)$ is a second order elliptic operator with real and symmetric coefficients. Assume that $A$ is {\it periodic} in $x_{d+1}$ and satisfies some minimal smoothness condition in the $x_{d+1}$ variable, we show that the $L^p$ Neumann and regularity problems are uniquely solvable for $1

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