Multidimensional lower bounds for the eigenvalues of Stokes and Dirichlet Laplacian operators

2012 ◽  
Vol 53 (4) ◽  
pp. 043508 ◽  
Author(s):  
Selma Yıldırım Yolcu ◽  
Türkay Yolcu
Keyword(s):  
Lower Bounds ◽  
Dirichlet Laplacian ◽  
Laplacian Operators

scholarly journals An uncertainty principle and lower bounds for the Dirichlet Laplacian on graphs

2019 ◽  
Vol 10 (1) ◽  
pp. 115-145
Author(s):  
H. Daniel Lenz ◽  
Peter Stollmann ◽  
Gunter Stolz
Keyword(s):  
Lower Bounds ◽  
Uncertainty Principle ◽  
Dirichlet Laplacian

scholarly journals Convex duality for principal frequencies

2021 ◽  
Vol 4 (4) ◽  
pp. 1-28
Author(s):  
Lorenzo Brasco ◽  
Keyword(s):  
Lower Bounds ◽  
Variational Formulation ◽  
Torsional Rigidity ◽  
First Eigenvalue ◽  
Convex Minimization Problem ◽  
Dirichlet Laplacian ◽  
The First Eigenvalue ◽  
Divergence Type ◽  
Poincaré Constant ◽  
Type Constraint

<abstract><p>We consider the sharp Sobolev-Poincaré constant for the embedding of $ W^{1, 2}_0(\Omega) $ into $ L^q(\Omega) $. We show that such a constant exhibits an unexpected dual variational formulation, in the range $ 1 &lt; q &lt; 2 $. Namely, this can be written as a convex minimization problem, under a divergence–type constraint. This is particularly useful in order to prove lower bounds. The result generalizes what happens for the torsional rigidity (corresponding to $ q = 1 $) and extends up to the case of the first eigenvalue of the Dirichlet-Laplacian (i.e., to $ q = 2 $).</p></abstract>

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Lower bounds on the dimension of the Rauzy gasket

2020 ◽  
Vol 148 (2) ◽  
pp. 321-327
Author(s):  
Rodolfo Gutiérrez-Romo ◽  
Carlos Matheus
Keyword(s):  
Lower Bounds

A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

10.37236/1188 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers

For $k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$ and on the k-color Ramsey numbers of $K_3$.

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