Convergence rates for elliptic reiterated homogenization problems

Jie Zhao

doi:10.3934/cpaa.2013.12.2787

Article Contents

2013, Volume 12, Issue 6: 2787-2795. Doi: 10.3934/cpaa.2013.12.2787

This issue Previous Article Existence and multiplicity of solutions for Kirchhoff type problem with critical exponent Next Article Analytic integrability for some degenerate planar systems

Convergence rates for elliptic reiterated homogenization problems

Jie Zhao^1,

1.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049

Received: February 29, 2012

Revised: August 31, 2012

Published: October 2013

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Abstract

In this paper, we study the convergence rates for the reiterated homogenization for equations of the form $-div(A(\frac{x}{\varepsilon},\frac{x}{\varepsilon^{2}})\nabla u_{\varepsilon})=f(x)$. As a consequence, we obtain the convergence rates in $L^{p}$ for solutions with Dirichlet boundary condition by a method based on the representation of elliptic equation solution by Green function. Meanwhile, the growth rate of Green function is found.

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Mathematics Subject Classification: Primary: 35J15; Secondary: 35J25.

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