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<p>We prove the existence and uniqueness of correctors for nonlinear homogenization problems associated with monotone operators of <i>p</i>-growth. The corrector equation is posed in the full space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^d\)</EquationSource> </InlineEquation>, as required in the non-periodic deterministic setting, and is solved within the framework of uniformly local Sobolev spaces. Our method relies on a localization procedure based on a sequence of increasing balls combined with the large mass trick, together with Caccioppoli-type estimates to establish compactness and stability. The results provide a foundation for extending deterministic homogenization theory beyond the periodic framework, ensuring that correctors exist and are uniquely defined in general heterogeneous media.</p>

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Existence and uniqueness of correctors for nonlinear homogenization in uniformly local Sobolev spaces

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  • 出版模式：

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  • 发表日期：

    2026年7月20日

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  • Achille Landri Pokam Kakeu,
  • Mapundi Kondwani Banda

摘要

We prove the existence and uniqueness of correctors for nonlinear homogenization problems associated with monotone operators of p-growth. The corrector equation is posed in the full space \(\mathbb {R}^d\) , as required in the non-periodic deterministic setting, and is solved within the framework of uniformly local Sobolev spaces. Our method relies on a localization procedure based on a sequence of increasing balls combined with the large mass trick, together with Caccioppoli-type estimates to establish compactness and stability. The results provide a foundation for extending deterministic homogenization theory beyond the periodic framework, ensuring that correctors exist and are uniquely defined in general heterogeneous media.