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arXiv · 1811.10024

On the first eigenvalue of the normalized p-Laplacian

Graziano Crasta·Ilaria Fragalà·Bernd Kawohl
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Abstract

We prove that, if $\Omega$ is an open bounded domain with smooth and connected boundary, for every $p \in (1, + \infty)$ the first Dirichlet eigenvalue of the normalized $p$-Laplacian is simple in the sense that two positive eigenfunctions are necessarily multiple of each other. We also give a (non-optimal) lower bound for the eigenvalue in terms of the measure of $\Omega$, and we address the open problem of proving a Faber-Krahn type inequality with balls as optimal domains.

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Graziano Crasta, Ilaria Fragalà, Bernd Kawohl. 2018-11-25. On the first eigenvalue of the normalized p-Laplacian. https://arxiv.org/abs/1811.10024

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