scholarly journals Estimates for the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice

2021 ◽  
Author(s):  
Anastasiia Legatiuk ◽  
Klaus Gürlebeck ◽  
Angela Hommel
Keyword(s):  
Fundamental Solution ◽  
Laplace Operator ◽  
Rectangular Lattice ◽  
Discrete Laplace Operator

scholarly journals Adaptive Discrete Laplace Operator

2011 ◽  
pp. 377-386 ◽  
Author(s):  
Christophe Fiorio ◽  
Christian Mercat ◽  
Frédéric Rieux
Keyword(s):  
Laplace Operator ◽  
Discrete Laplace Operator

Discrete Laplace operator of 3-cochains

2020 ◽  
pp. 2150001
Author(s):  
Azeddine Baalal ◽  
Khalid Hatim
Keyword(s):  
Simplicial Complex ◽  
Essential Spectrum ◽  
Laplace Operator ◽  
Upper Bound ◽  
Discrete Laplacian ◽  
Discrete Laplace Operator

In this paper, we use the Nelson lemma to give a new proof for the essential self-adjointness of the discrete Laplace operator acting on 3-cochains, which we are defined in our previous paper [A. Baalal and K. Hatim, The discrete Laplacian of a 3-simplicial complex (2019), https://hal.archives-ouvertes.fr/hal-02105789 ]. Moreover, we establish on the infimum of the essential spectrum an upper bound.

scholarly journals Optimal codomains for the Laplace operator and the product Laplace operator

2007 ◽  
Vol 5 (3) ◽  
pp. 269-285
Author(s):  
Josefina Alvarez ◽  
Lloyd Edgar S. Moyo
Keyword(s):  
Fundamental Solution ◽  
Laplace Operator ◽  
Euclidean Case ◽  
Product Domain ◽  
Space Of Distributions ◽  
The Laplace Operator ◽  
Maximal Space

An optimal codomain for an operatorP(∂)with fundamental solutionE, is a maximal space of distributionsTfor which it is possible to define the convolutionE*Tand thus to solve the equationP(∂)S=T. We identify optimal codomains for the Laplace operator in the Euclidean case and for the product Laplace operator in the product domain case. The convolution is understood in the sense of theS′-convolution.

scholarly journals Codomains for the Cauchy-Riemann and Laplace operators inℝ2

2008 ◽  
Vol 6 (1) ◽  
pp. 71-87
Author(s):  
Lloyd Edgar S. Moyo
Keyword(s):  
Differential Operator ◽  
Fundamental Solution ◽  
Laplace Operator ◽  
Constant Coefficient ◽  
Partial Differential Operator ◽  
Linear Partial Differential Operator ◽  
Partial Differential ◽  
Nonzero Constant ◽  
Space Of Distributions ◽  
Cauchy Riemann

A codomain for a nonzero constant-coefficient linear partial differential operatorP(∂)with fundamental solutionEis a space of distributionsTfor which it is possible to define the convolutionE*Tand thus solving the equationP(∂)S=T. We identify codomains for the Cauchy-Riemann operator inℝ2and Laplace operator inℝ2. The convolution is understood in the sense of theS′-convolution.

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