scholarly journals An alternative proof of lower bounds for the first eigenvalue on manifolds

2017 ◽  
Vol 290 (16) ◽  
pp. 2708-2713 ◽  
Author(s):  
Yuntao Zhang ◽  
Kui Wang
Keyword(s):  
Lower Bounds ◽  
Alternative Proof ◽  
First Eigenvalue ◽  
The First Eigenvalue

scholarly journals Principal frequency of the p-Laplacian and the inradius of Euclidean domains

2015 ◽  
Vol 07 (03) ◽  
pp. 505-511 ◽  
Author(s):  
Guillaume Poliquin
Keyword(s):  
Lower Bound ◽  
Laplace Operator ◽  
Lower Bounds ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
Planar Domains ◽  
Principal Frequency ◽  
The Laplace Operator ◽  
Simply Connected ◽  
Euclidean Domains

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.

scholarly journals Lower bounds for the first eigenvalue of the magnetic Laplacian

2018 ◽  
Vol 274 (10) ◽  
pp. 2818-2845 ◽  
Author(s):  
Bruno Colbois ◽  
Alessandro Savo
Keyword(s):  
Lower Bounds ◽  
First Eigenvalue ◽  
The First Eigenvalue
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