scholarly journals Spectral properties of the Laplace operator with respect to electric and magnetic boundary conditions

1983 ◽  
Vol 92 (1) ◽  
pp. 1-65 ◽  
Author(s):  
P Werner
Keyword(s):  
Boundary Conditions ◽  
Laplace Operator ◽  
Spectral Properties ◽  
The Laplace Operator

scholarly journals Spectral properties of the generalised Samarskii-Ionkin type problems

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 1019-1024
Author(s):  
Nurgissa Yessirkegenov
Keyword(s):  
Boundary Conditions ◽  
Explicit Form ◽  
Laplace Operator ◽  
Spectral Properties ◽  
The Laplace Operator

In this paper, we study spectral properties of the Laplace operator with generalised Samarskii-Ionkin boundary conditions in a disk. The eigenfunctions and eigenvalues of these problems are constructed in the explicit form. Moreover, we prove the completeness of these eigenfunctions

scholarly journals On a Differential Inclusion Involving Dirichlet–Laplace Operators of Fractional Orders

2020 ◽  
Vol 43 (6) ◽  
pp. 4089-4106
Author(s):  
Rafał Kamocki
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusion ◽  
Laplace Operator ◽  
Spectral Decomposition ◽  
Convex Analysis ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Fenchel Transform ◽  
The Laplace Operator ◽  
Fractional Orders

Abstract In this paper, we investigate a nonlinear differential inclusion with Dirichlet boundary conditions containing a weak Laplace operator of fractional orders (defined via the spectral decomposition of the Laplace operator $$-{\varDelta }$$ - Δ under Dirichlet boundary conditions). Using variational methods, we characterize solutions of such a problem. Our approach is based on tools from convex analysis (properties of a Legendre–Fenchel transform).

scholarly journals DISCRETIZED LAPLACIANS ON AN INTERVAL AND THEIR RENORMALIZATION GROUP

1994 ◽  
Vol 09 (25) ◽  
pp. 4485-4509 ◽  
Author(s):  
E. ERCOLESSI ◽  
P. TEOTONIO-SOBRINHO ◽  
G. BIMONTE
Keyword(s):  
Boundary Conditions ◽  
Laplace Operator ◽  
Continuum Limit ◽  
Wave Functions ◽  
The Other ◽  
Scale Invariant ◽  
Dimensional Parameter ◽  
Finite Dimensional ◽  
The Laplace Operator ◽  
The Continuum

The Laplace operator admits infinite self-adjoint extensions when considered on a segment of the real line. They have different domains of essential self-adjointness characterized by a suitable set of boundary conditions on the wave functions. In this paper we show how these extensions can be recovered by studying the continuum limit of certain discretized versions of the Laplace operator on a lattice. Associated to this limiting procedure, there is a renormalization flow in the finite-dimensional parameter space describing the discretized operators. This flow is shown to have infinite fixed points, corresponding to the self-adjoint extensions characterized by scale-invariant boundary conditions. The other extensions are recovered by looking at the other trajectories of the flow.

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