We introduce the signless 1-Laplacian and the dual Cheeger constant on simplicial complexes. The connection of its spectrum to the combinatorial properties like independence number, chromatic number and dual Cheeger constant is investigated. Our estimates can be comparable to Hoffman's bounds on ...
Motivated by extremal problems of weighted Dirichlet or Neumann eigenvalues, we will establish two fundamental results on the dependence of weighted eigenvalues of the one-dimensional p-Laplacian on indefinite integrable weights. One is the continuous differentiability of eigenvalues in weights in the Lebe...
We discuss the harmonicity of horizontally conformal maps and their relations with the spectrum of the Laplacian. We prove that if Φ:M→N is a horizontally conformal map such that the tension field is divergence free, then Φ is harmonic. Furthermore, if N is noncompact, then Φ must be...
For any Lipschitz domain we construct an arbitrarily small, localized perturbation which splits the spectrum of the Dirichlet, Neumann or Robin Laplacian into simple eigenvalues. We showcase two different approaches. The first one consists in the excision of a hole inside the domain and the ...
On the spectrum of the p-Laplacian operator for Neumann eigenvalue problems with weights Tsouli. On the spectrum of the p-Laplacian operator for Neumann eigen- value problems with weights. In Proceedings of the 2005 Oujda International ... SE Habib,T Najib - 《Electronic Journal of Differential...
We prove that the spectrum of the infinite-dimensional Laplacian is the left half plane {λ∈C:Re λ≦0}. As a consequence, we obtain a simple proof of the norm discontinuity of the generated semigroup. This is a preview of subscription content, log in via an institution to check access...
On the Fučik spectrum of the p-Laplacian with indefinite weights. (English).We study the Fucˇik spectrum Σ of the one-dimensional p-Laplacian with indefinite weights. Some new results concerning the description and the asymptotic behaviour of Σ are obtained. To cite this article: M.Alif...
1 1. INTRODUCTION The Laplacian matrix of a graph and its eigenvalues can be used in several areas of mathematical research and have a physical interpretation in various physical and chemical theories. The related matrix — the adjacency matrix of a graph and its eigenvalues were much more ...
The Laplacian matrix $L(G)=D(G)-A(G)$ is the difference of the diagonal matrix of vertex degrees and the 0-1 adjacency matrix. Various aspects of the spectrum of L(G) are investigated. Particular attention is given to multiplicities of integer eigenvalues and to the effect on the ...
Consider the Schrdinger operator Δ + V in L 2 ( n ) with a potential V , locally integrable and semibounded below. As we mentioned in Sect.16.6, Molchanov's criterion (16.6.2) involves the so-called negligible sets F , that is, sets of sufficiently small harmonic capacity....