On the nodal set conjecture for the $p$-Laplacian in circularly symmetric domains

Vladimir Bobkov

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arXiv · 2602.01210

On the nodal set conjecture for the $p$-Laplacian in circularly symmetric domains

Vladimir Bobkov

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Abstract

In 1990, P\"utter shown that the nodal line of any second eigenfunction of the Dirichlet Laplacian on a planar bounded simply connected domain $\Omega$ intersects the boundary $\partial\Omega$ provided $\Omega$ has the circular symmetry. By adopting the method of moving polarization, we establish similar information on the nodal set of second eigenfunctions of the Dirichlet $p$-Laplacian on circularly symmetric domains in arbitrary higher dimension.

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Vladimir Bobkov. 2026-02-01. On the nodal set conjecture for the $p$-Laplacian in circularly symmetric domains. https://arxiv.org/abs/2602.01210

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