Principal frequency of the p-Laplacian and the inradius of Euclidean\n domains

2014/10/04 by Guillaume Poliquin, Poliquin, Guillaume · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1410.1098

openalex publication_date 2014/10/04 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

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

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