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<p>We prove antisymmetric maximum principles and Hopf-type lemmas for linear problems described by the Logarithmic Laplacian. As application, we prove the symmetry of solutions for semilinear problems in symmetric sets, and a rigidity result for the parallel surface problem for the Logarithmic Laplacian.</p>

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Antisymmetric maximum principles and Hopf’s lemmas for the Logarithmic Laplacian, with applications to symmetry results

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月27日

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  • Luigi Pollastro,
  • Nicola Soave

摘要

We prove antisymmetric maximum principles and Hopf-type lemmas for linear problems described by the Logarithmic Laplacian. As application, we prove the symmetry of solutions for semilinear problems in symmetric sets, and a rigidity result for the parallel surface problem for the Logarithmic Laplacian.