Homogenization of the Neumann Problem for Elliptic Systems with Periodic Coefficients

  title={Homogenization of the Neumann Problem for Elliptic Systems with Periodic Coefficients},
  author={Tatiana Suslina},
  journal={SIAM J. Math. Anal.},
  • T. Suslina
  • Published 5 December 2012
  • Mathematics
  • SIAM J. Math. Anal.
Let ${\mathcal O} \subset {\mathbb R}^d$ be a bounded domain with the boundary of class $C^{1,1}$. In $L_2({\mathcal O};{\mathbb C}^n)$, a matrix elliptic second order differential operator ${\mathcal A}_{N,\varepsilon}$ with the Neumann boundary condition is considered. Here $\varepsilon>0$ is a small parameter; the coefficients of ${\mathcal A}_{N,\varepsilon}$ are periodic and depend on ${\mathbf x} /\varepsilon$. There are no regularity assumptions on the coefficients. It is shown that the… 
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