scholarly journals An isoperimetric inequality for the second eigenvalue of the Laplacian with Robin boundary conditions

2008 ◽  
Vol 137 (02) ◽  
pp. 627-633 ◽  
Author(s):  
James Kennedy
Keyword(s):  
Boundary Conditions ◽  
Isoperimetric Inequality ◽  
Robin Boundary Conditions ◽  
Robin Boundary ◽  
Second Eigenvalue

scholarly journals ON AN EIGENVALUE PROBLEM INVOLVING THE HARDY POTENTIAL

2010 ◽  
Vol 12 (06) ◽  
pp. 953-975 ◽  
Author(s):  
J. CHABROWSKI ◽  
I. PERAL ◽  
B. RUF
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Principal Eigenvalue ◽  
Robin Boundary Conditions ◽  
Robin Problem ◽  
Hardy Potential ◽  
High Dimensions ◽  
The Neumann Problem ◽  
Robin Boundary ◽  
Second Eigenvalue

In this note we consider the eigenvalue problem for the Laplacian with the Neumann and Robin boundary conditions involving the Hardy potential. We prove the existence of eigenfunctions of the second eigenvalue for the Neumann problem and of the principal eigenvalue for the Robin problem in "high" dimensions.

scholarly journals An efficient adaptive grid method for a system of singularly perturbed convection-diffusion problems with Robin boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Li-Bin Liu ◽  
Ying Liang ◽  
Xiaobing Bao ◽  
Honglin Fang
Keyword(s):  
Boundary Conditions ◽  
Grid Method ◽  
Posteriori Error ◽  
Adaptive Grid ◽  
Singularly Perturbed ◽  
Robin Boundary Conditions ◽  
Euler Formula ◽  
Convection Diffusion ◽  
Backward Euler ◽  
Robin Boundary

AbstractA system of singularly perturbed convection-diffusion equations with Robin boundary conditions is considered on the interval $[0,1]$ [ 0 , 1 ] . It is shown that any solution of such a problem can be expressed to a system of first-order singularly perturbed initial value problem, which is discretized by the backward Euler formula on an arbitrary nonuniform mesh. An a posteriori error estimation in maximum norm is derived to design an adaptive grid generation algorithm. Besides, in order to establish the initial values of the original problems, we construct a nonlinear optimization problem, which is solved by the Nelder–Mead simplex method. Numerical results are given to demonstrate the performance of the presented method.

scholarly journals Logarithmic minimal models with Robin boundary conditions

2016 ◽  
Vol 2016 (6) ◽  
pp. 063104 ◽  
Author(s):  
Jean-Emile Bourgine ◽  
Paul A Pearce ◽  
Elena Tartaglia
Keyword(s):  
Boundary Conditions ◽  
Robin Boundary Conditions ◽  
Minimal Models ◽  
Robin Boundary
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