Principal frequency of the $p$-Laplacian and the inradius of Euclidean domains

Guillaume Poliquin

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arXiv · 1410.1098

Principal frequency of the $p$-Laplacian and the inradius of Euclidean domains

Guillaume Poliquin

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Abstract

We study the lower bounds for the principal frequency of the $p$-Laplacian on $N$-dimensional Euclidean domains. For $p>N$, we obtain a lower bound for the first eigenvalue of the $p$-Laplacian in terms of its inradius, without any assumptions on the topology of the domain. Moreover, we show that a similar lower bound can be obtained if $p > N-1$ assuming the boundary is connected. This result can be viewed as a generalization of the classical bounds for the first eigenvalue of the Laplace operator on simply connected planar domains.

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BibTeX RIS

Guillaume Poliquin. 2014-10-04. Principal frequency of the $p$-Laplacian and the inradius of Euclidean domains. https://arxiv.org/abs/1410.1098

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