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 language | English (US) |
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Pages (from-to) | 93-107 |
Number of pages | 15 |
Journal | Applied Mathematics & Optimization |
Volume | 15 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1987 |
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics