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<p>We consider weighted Hardy inequalities involving the distance function to the boundary of a domain in the <i>N</i>-dimensional Euclidean space with nonempty boundary. We give a lower bound for the corresponding best Hardy constant for a domain satisfying a uniform exterior cone condition. This lower bound depends on the aperture of the corresponding infinite circular cone.</p>

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A Lower Bound for the Weighted Hardy Constant for Domains Satisfying a Uniform Exterior Cone Condition

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月18日

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  • Ujjal Das,
  • Yehuda Pinchover

摘要

We consider weighted Hardy inequalities involving the distance function to the boundary of a domain in the N-dimensional Euclidean space with nonempty boundary. We give a lower bound for the corresponding best Hardy constant for a domain satisfying a uniform exterior cone condition. This lower bound depends on the aperture of the corresponding infinite circular cone.