scholarly journals On odd Laplace operators. II

2004 ◽  
pp. 179-205 ◽  
Author(s):  
Hovhannes M. Khudaverdian ◽  
Theodore Voronov
Keyword(s):  
Laplace Operators

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
pp. 85-104
Author(s):  
Shakirbai G. Kasimov ◽  
◽  
Mahkambek M. Babaev ◽  
◽  
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Laplace Operators ◽  
Initial Boundary Problem ◽  
Initial Boundary Value ◽  
Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

On eigenvalue problem of the Laplace operators for ellipsoidal areas

2018 ◽  
Vol 2018 (1) ◽  
pp. 146-154
Author(s):  
D.G. Rakhimov ◽  
◽  
Sh.M. Suyarov ◽  
Keyword(s):  
Eigenvalue Problem ◽  
Laplace Operators

scholarly journals p-Laplace Operators for Oriented Hypergraphs

2021 ◽  
Author(s):  
Jürgen Jost ◽  
Raffaella Mulas ◽  
Dong Zhang
Keyword(s):  
Laplace Operator ◽  
Spectral Properties ◽  
General Setting ◽  
Laplace Operators

AbstractThe p-Laplacian for graphs, as well as the vertex Laplace operator and the hyperedge Laplace operator for the general setting of oriented hypergraphs, are generalized. In particular, both a vertex p-Laplacian and a hyperedge p-Laplacian are defined for oriented hypergraphs, for all p ≥ 1. Several spectral properties of these operators are investigated.

Vectors and Functions and Operators

2020 ◽  
pp. 3-13
Author(s):  
Jochen Autschbach
Keyword(s):  
Linear Algebra ◽  
Scalar Product ◽  
Cross Product ◽  
Eigenvalues And Eigenvectors ◽  
Laplace Operators

This chapter introduces – briefly – vectors and functions and the similarities between them, some basic linear algebra concepts, operators (including the del and Laplace operators), eigenvalues and eigenvectors &eigenfunctions, the scalar (dot) and vector (cross) product between two vectors, the scalar product between two functions, the concepts of normalization, orthogonality, and orthonormality. The concept of an operator is first introduced by considering the rotation and stretching or compression of a vector. It is then generalized to a mathematical prescription that changes a function into another function.

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