## Abstract

We consider the homogenization problem {Mathematical expression} where D is a bounded domain, a is a C^{1,α}, periodic, uniformly positive matrix, and the data g belongs to L^{p}(∂D), 1 <p < ∞. We show that, if ∂D satisfies a uniform exterior sphere condition, then u_{ε}converges in L^{p}(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

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