scholarly journals The Laplace operator on the Sierpinski gasket with Robin boundary conditions

2017 ◽  
Vol 38 ◽  
pp. 245-260 ◽  
Author(s):  
Brigitte E. Breckner ◽  
Ralph Chill
Keyword(s):  
Boundary Conditions ◽  
Laplace Operator ◽  
Sierpinski Gasket ◽  
Robin Boundary Conditions ◽  
Sierpiński Gasket ◽  
The Laplace Operator ◽  
Robin Boundary

scholarly journals Explicit Spectral Decimation for a Class of Self-Similar Fractals

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Sergio A. Hernández ◽  
Federico Menéndez-Conde
Keyword(s):  
Laplace Operator ◽  
Sierpinski Gasket ◽  
Higher Dimensions ◽  
Explicit Construction ◽  
Sierpiński Gasket ◽  
Infinite Collection ◽  
Self Similar ◽  
The Laplace Operator

The method of spectral decimation is applied to an infinite collection of self-similar fractals. The sets considered are a generalization of the Sierpinski Gasket to higher dimensions; they belong to the class of nested fractals and are thus very symmetric. An explicit construction is given to obtain formulas for the eigenvalues of the Laplace operator acting on these fractals.

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 Regular eigenvalue problem with eigenparameter contained in the equation and the boundary conditions

1990 ◽  
Vol 13 (4) ◽  
pp. 651-659 ◽  
Author(s):  
E. M. E. Zayed ◽  
S. F. M. Ibrahim
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Bounded Domain ◽  
Smooth Boundary ◽  
Robin Boundary Conditions ◽  
Expansion Theorem ◽  
Eigenvalue Parameter ◽  
The Laplace Operator ◽  
Simply Connected ◽  
Robin Boundary

The purpose of this paper is to establish the expansion theorem for a regular right-definite eigenvalue problem for the Laplace operator inRn,(n≥2)with an eigenvalue parameterλcontained in the equation and the Robin boundary conditions on two “parts” of a smooth boundary of a simply connected bounded domain.

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