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<p>Our aim in this paper is to provide a detailed proof of the existence of the corrector, based on the existence of local weak solutions to linear problems. We seek the solution of a second-order linear partial differential equation in divergence form in the usual sense of distribution. The obtained result represents a significant step towards the numerical implementation of deterministic homogenization theory results beyond the periodic setting.</p>

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CORRECTOR PROBLEM IN THE SPACE OF LOCALLY UNIFORMLY BOUNDED FUNCTIONS AND APPLICATIONS

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月31日

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  • Achille Landri Pokam Kakeu,
  • Mapundi Kondwani Banda

摘要

Our aim in this paper is to provide a detailed proof of the existence of the corrector, based on the existence of local weak solutions to linear problems. We seek the solution of a second-order linear partial differential equation in divergence form in the usual sense of distribution. The obtained result represents a significant step towards the numerical implementation of deterministic homogenization theory results beyond the periodic setting.