scholarly journals About Bounds for Eigenvalues of the Laplacian with Density

2020 ◽  
Author(s):  
Aïssatou Mossèle Ndiaye ◽  
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Keyword(s):  
Eigenvalues Of The Laplacian

scholarly journals Extrema of Low Eigenvalues of the Dirichlet–Neumann Laplacian on a Disk

2010 ◽  
Vol 62 (4) ◽  
pp. 808-826
Author(s):  
Eveline Legendre
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Neumann Boundary ◽  
Mixed Boundary Conditions ◽  
First Eigenvalue ◽  
Bounded Number ◽  
Eigenvalues Of The Laplacian ◽  
Neumann Laplacian ◽  
Dirichlet And Neumann Conditions ◽  
Second Eigenvalue

AbstractWe study extrema of the first and the second mixed eigenvalues of the Laplacian on the disk among some families of Dirichlet–Neumann boundary conditions. We show that the minimizer of the second eigenvalue among all mixed boundary conditions lies in a compact 1-parameter family for which an explicit description is given. Moreover, we prove that among all partitions of the boundary with bounded number of parts on which Dirichlet and Neumann conditions are imposed alternately, the first eigenvalue is maximized by the uniformly distributed partition.

Shape Recognition Based on Eigenvalues of the Laplacian

2011 ◽  
pp. 185-254 ◽  
Author(s):  
Mohamed Ben Haj Rhouma ◽  
Mohamed Ali Khabou ◽  
Lotfi Hermi
Keyword(s):  
Shape Recognition ◽  
Eigenvalues Of The Laplacian
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