Bounds on the Principal Frequency of the $p$-Laplacian

Guillaume Poliquin

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arXiv · 1304.5131

Bounds on the Principal Frequency of the $p$-Laplacian

Guillaume Poliquin

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Abstract

This paper is concerned with the lower bounds for the principal frequency of the $p$-Laplacian on $n$-dimensional Euclidean domains. In particular, we extend the classical results involving the inner radius of a domain and the first eigenvalue of the Laplace operator to the case $p\neq2$. As a by-product, we obtain a lower bound on the size of the nodal set of an eigenfunction of the $p$-Laplacian on planar domains.

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BibTeX RIS

Guillaume Poliquin. 2014-10-01. Bounds on the Principal Frequency of the $p$-Laplacian. https://arxiv.org/abs/1304.5131

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