Related papers: Eigenvalue estimates for the higher order buckling…
We prove lower bounds for the Dirichlet Laplacian on possibly unbounded domains in terms of natural geometric conditions. This is used to derive uncertainty principles for low energy functions of general elliptic second order divergence…
We obtain tight upper and lower bounds to the eigenvalues of an anharmonic oscillator with a rational potential. We compare our bounds with results given by other approaches.
We consider the problem of estimating the eigenvalues and the integral of the corresponding eigenfunctions, associated to the Newtonian potential operator, defined in a bounded domain $\Omega \subset \mathbb{R}^{d},$ where $d = 2, 3$, in…
We consider a class of eigenvalue problems for poly-harmonic operators, including Dirichlet and buckling-type eigenvalue problems. We prove an analyticity result for the dependence of the symmetric functions of the eigenvalues upon domain…
In this paper, we revisit McLaughlin's inverse problem, which consists in the recovery of the fourth-order differential operator from the eigenvalues and two sequences of weight numbers. We for the first time prove the uniqueness for…
The purpose of this article is to approximately compute the eigenvalues of the symmetric Dirichlet Laplacian within an interval $(0,\Lambda)$. A novel domain decomposition Ritz method, partition of unity condensed pole interpolation method,…
A method to compute guaranteed lower bounds to the eigenvalues of the Maxwell system in two or three space dimensions is proposed as a generalization of the method of Liu and Oishi [SIAM J. Numer. Anal., 51, 2013] for the Laplace operator.…
This article is devoted to computing the lower and upper bounds of the Laplace eigenvalue problem. By using the special nonconforming finite elements, i.e., enriched Crouzeix-Raviart element and extension $Q_1^{\rm rot}$, we get the lower…
We establish two universal inequalities for Dirichlet eigenvalues of the Laplacian on a Euclidean convex domain.
In this paper, we consider the obstacle problem for the fractional Laplace operator $(-\Delta)^s$ in the Euclidian space $\mathbb{R}^n$ in the case where $1<s<2$. As first observed in \cite{Y}, the problem can be extended to the upper…
We present exact expressions for the eigenvalues and eigenvectors of the d-dimensional Laplace operator in a cut Fock basis.
In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we…
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.
The dependence on the domain is studied for the Dirichlet eigenvalues of an elliptic operator considered in bounded domains. Their proximity is measured by a norm of the difference of two orthogonal projectors corresponding to the reference…
In this article we study the stability problem for positive quaternion-K\"ahler manifolds. We give a description of infinitesimal Einstein deformations and destabilising directions in terms of Laplace eigenfunctions and a special class of…
In this paper, we consider the eigenvalue problem for Hodge-Laplacian on a Riemannian manifold $M$ isometrically immersed into another Riemannian manifold $\bar M$ for arbitrary codimension. We first assume the pull back Weitzenb\"{o}ck…
We consider a Riemannian cylinder endowed with a closed potential 1-form A and study the magnetic Laplacian with magnetic Neumann boundary conditions associated with those data. We establish a sharp lower bound for the first eigenvalue and…
Recently, there has been interest in high-precision approximations of the first eigenvalue of the Laplace-Beltrami operator on spherical triangles for combinatorial purposes. We compute improved and certified enclosures to these…
In this paper we introduce the magnetic Hodge Laplacian, which is a generalization of the magnetic Laplacian on functions to differential forms. We consider various spectral results, which are known for the magnetic Laplacian on functions…
This paper reviews many of the known inequalities for the eigenvalues of the Laplacian and bi-Laplacian on bounded domains in Euclidean space. In particular, we focus on isoperimetric inequalities for the low eigenvalues of the Dirichlet…