Homogenization of elliptic problems with Lp boundary data

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Abstract

We consider the homogenization problem {Mathematical expression} where D is a bounded domain, a is a C1,α, periodic, uniformly positive matrix, and the data g belongs to Lp(∂D), 1 <p < ∞. We show that, if ∂D satisfies a uniform exterior sphere condition, then uεconverges in Lp(D) to the solution of the corresponding homogenized problem as ε → 0. The proof is done via estimates for Poisson's kernel. We give examples showing that this convergence result does not hold for a general G-convergent sequence of operators and depends on the periodicity of a as well as on its smoothness.

Original languageEnglish (US)
Pages (from-to)93-107
Number of pages15
JournalApplied Mathematics & Optimization
Volume15
Issue number1
DOIs
StatePublished - Jan 1987

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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