We prove that if Ω is an open bounded domain with smooth and connected boundary, for every p ∈(1,+∞) 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 (nonoptimal) lower bound for the eigenvalue in terms of the measure of Ω, and we address the open problem of proving a Faber-Krahn-type inequality with balls as optimal domains.
On the first eigenvalue of the normalized p-laplacian / Crasta, G.; Fragala, I.; Kawohl, B.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 148:2(2020), pp. 577-590. [10.1090/proc/14823]
On the first eigenvalue of the normalized p-laplacian
Crasta G.;
2020
Abstract
We prove that if Ω is an open bounded domain with smooth and connected boundary, for every p ∈(1,+∞) 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 (nonoptimal) lower bound for the eigenvalue in terms of the measure of Ω, and we address the open problem of proving a Faber-Krahn-type inequality with balls as optimal domains.| File | Dimensione | Formato | |
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Note: https://www.ams.org/journals/proc/2020-148-02/S0002-9939-2019-14823-1/
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