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<p>Using the domain variation estimate, we give a new proof of the local Pohozaev identities for weak solutions of elliptic equations involving <i>p</i>-Laplacian operators under only <i>C</i><sup>1</sup>-regularity of the solutions. As an application, we obtain the Pohozaev identities for <i>C</i><sup>1</sup> solution of <i>p</i>-Laplacian equation in ℝ<sup><i>N</i></sup> with 1 &lt; <i>p</i> &lt; <i>N</i>.</p>

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Domain variations and Pohozaev identities for weak solutions of p-Laplacian equation

  • 期刊论文

  • 发表日期：

    2025年10月28日

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  • Shusen Yan,
  • Huansong Zhou

摘要

Using the domain variation estimate, we give a new proof of the local Pohozaev identities for weak solutions of elliptic equations involving p-Laplacian operators under only C1-regularity of the solutions. As an application, we obtain the Pohozaev identities for C1 solution of p-Laplacian equation in ℝN with 1 < p < N.