scholarly journals Comparison results for solutions to the anisotropic Laplacian with Robin boundary conditions

2022 ◽  
Vol 214 ◽  
pp. 112615
Author(s):  
Rossano Sannipoli
Keyword(s):  
Boundary Conditions ◽  
Robin Boundary Conditions ◽  
Comparison Results ◽  
Robin Boundary

scholarly journals Comparison results for solutions to p-Laplace equations with Robin boundary conditions

2021 ◽  
Author(s):  
Vincenzo Amato ◽  
Andrea Gentile ◽  
Alba Lia Masiello
Keyword(s):  
Boundary Conditions ◽  
Laplace Operator ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Robin Boundary Conditions ◽  
Planar Case ◽  
Laplace Equations ◽  
Comparison Results ◽  
Robin Boundary ◽  
Appl Math

AbstractIn the last decades, comparison results of Talenti type for Elliptic Problems with Dirichlet boundary conditions have been widely investigated. In this paper, we generalize the results obtained in Alvino et al. (Commun Pure Appl Math, to appear) to the case of p-Laplace operator with Robin boundary conditions. The point-wise comparison, obtained in Alvino et al. (to appear) only in the planar case, holds true in any dimension if p is sufficiently small.

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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