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<p>We discuss simple and short proofs of identities that give the classical Poincaré and Hardy inequalities with sharp constants. These equalities directly imply characterization of nontrivial optimizers for the corresponding inequalities. Our proofs are independent of the polar coordinates in the integral and geometry of the domain.</p>

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On Hardy-Poincaré Inequalities

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月1日

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  • Tohru Ozawa,
  • Durvudkhan Suragan

摘要

We discuss simple and short proofs of identities that give the classical Poincaré and Hardy inequalities with sharp constants. These equalities directly imply characterization of nontrivial optimizers for the corresponding inequalities. Our proofs are independent of the polar coordinates in the integral and geometry of the domain.