Upper bound for the first nonzero eigenvalue related to the p-Laplacian

2020 ◽  
Vol 130 (1) ◽  
Author(s):  
Sheela Verma
Keyword(s):  
Upper Bound ◽  
Nonzero Eigenvalue

Spectral gap of a weighted 3-simplicial complex

2021 ◽  
pp. 2150084
Author(s):  
Khalid Hatim ◽  
Azeddine Baalal
Keyword(s):  
Lower Bound ◽  
Simplicial Complex ◽  
Upper Bound ◽  
Spectral Gap ◽  
Simplicial Complexes ◽  
Cheeger Constant ◽  
Nonzero Eigenvalue ◽  
New Framework

In this paper, we construct a new framework that’s we call the weighted [Formula: see text]-simplicial complex and we define its spectral gap. An upper bound for our spectral gap is given by generalizing the Cheeger constant. The lower bound for our spectral gap is obtained from the first nonzero eigenvalue of the Laplacian acting on the functions of certain weighted [Formula: see text]-simplicial complexes.

scholarly journals REILLY INEQUALITIES OF ELLIPTIC OPERATORS ON CLOSED SUBMANIFOLDS

2009 ◽  
Vol 80 (2) ◽  
pp. 335-346
Author(s):  
RUSHAN WANG
Keyword(s):  
Elliptic Operator ◽  
Sectional Curvature ◽  
Riemannian Manifolds ◽  
Upper Bound ◽  
Vector Fields ◽  
Elliptic Operators ◽  
Position Vector ◽  
Space Forms ◽  
Nonzero Eigenvalue ◽  
Closed Hypersurfaces

AbstractUsing generalized position vector fields we obtain new upper bound estimates of the first nonzero eigenvalue of a kind of elliptic operator on closed submanifolds isometrically immersed in Riemannian manifolds of bounded sectional curvature. Applying these Reilly inequalities we improve a series of recent upper bound estimates of the first nonzero eigenvalue of the Lr operator on closed hypersurfaces in space forms.

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