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

Luigi Pollastro; Nicola Soave

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arXiv · 2407.11718

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

Luigi Pollastro·Nicola Soave

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Abstract

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.

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Luigi Pollastro, Nicola Soave. 2024-07-16. Antisymmetric maximum principles and Hopf's lemmas for the Logarithmic Laplacian, with applications to symmetry results. https://arxiv.org/abs/2407.11718

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