相关论文: Estimates for the Lowest Eigenvalue of Magnetic La…

The aim of the present paper is to investigate the behavior of the spectrum of the Neumann Laplacian in domains with little holes excised from the interior. More precisely, we consider the eigenvalues of the Laplacian with homogeneous…

We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from the ball. This expression implies an estimate as exact as you want…

It is widely known that the spectrum of the Dirichlet Laplacian is stable under small perturbations of a domain, while in the case of the Neumann or mixed boundary conditions the spectrum may abruptly change. In this work we discuss an…

In this paper we study inverse boundary value problems with partial data for the bi-harmonic operator with first order perturbation. We consider two types of subsets of $\mathbb{R}^{n}(n\geq 3)$, one is an infinite slab, the other is a…

In this paper, we obtain lower bounds for the first eigenvalue to some kinds of the eigenvalue problems for Bi-drifted Laplacian operator on compact manifolds (also called a smooth metric measure space) with boundary and $m$-Bakry-Emery…

In this paper, we give a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic $1$-forms defined on a compact manifold whose boundary is endowed with a Riemannian flow. The limiting case gives rise to a…

Ten sharp lower estimates of the first non-trivial eigenvalue of Laplacian on compact Riemannian manifolds are reviewed and compared. An improved variational formula, a general common estimate, and a new sharp one are added. The best lower…

Let $M$ be a closed hypersurface in $\mathbb{R}^{n}$ and $\Omega$ be a bounded domain such that $M= \partial\Omega$. In this article, we obtain an upper bound for the first non-zero eigenvalue of the following problems. \begin{itemize}…

In the present paper, we study the first eigenvalue $\lambda(p)$ of the one-dimensional $p$-Laplacian in the interval $(-1,1)$. We give an upper and lower estimate of $\lambda(p)$ and study its asymptotic behavior as $p \to 1+0$ or $p \to…

In this paper we prove an optimal upper bound for the first eigenvalue of a Robin-Neumann boundary value problem for the p-Laplacian operator in domains with convex holes. An analogous estimate is obtained for the corresponding torsional…

Among all triangles of given diameter, the equilateral triangle is shown to minimize the sum of the first $n$ eigenvalues of the Dirichlet Laplacian, for each $n \geq 1$. In addition, the first, second and third eigenvalues are each proved…

This paper deals with the Neumann eigenvalue problem for the Hermite operator defined in a convex, possibly unbounded, planar domain $\Omega$, having one axis of symmetry passing through the origin. We prove a sharp lower bound for the…

We consider the Laplacian in a domain squeezed between two parallel hypersurfaces in Euclidean spaces of any dimension, subject to Dirichlet boundary conditions on one of the hypersurfaces and Neumann boundary conditions on the other. We…

We continue the analysis started in [Noris,Terracini,Indiana Univ Math J,2010] and [Bonnaillie-No\"el,Noris,Nys,Terracini,Analysis & PDE,2014], concerning the behavior of the eigenvalues of a magnetic Schr\"odinger operator of Aharonov-Bohm…

We consider a magnetic Laplacian $-\Delta_A=(id+A)^\star (id+A)$ on a noncompact hyperbolic surface $\mM $ with finite area. $A$ is a real one-form and the magnetic field $dA$ is constant in each cusp. When the harmonic component of $A$…

We prove P\'olya's conjecture for the eigenvalues of the Dirichlet Laplacian on annular domains. Our approach builds upon and extends the methods we previously developed for disks and balls. It combines variational bounds, estimates of…

We prove sharp isoperimetric inequalities for Neumann eigenvalues of the Laplacian on triangular domains. The first nonzero Neumann eigenvalue is shown to be maximal for the equilateral triangle among all triangles of given perimeter, and…

We prove a lower bound estimate for the first non-zero eigenvalue of the Witten-Laplacian on compact Riemannian manifolds. As an application, we derive a lower bound estimate for the diameter of compact gradient shrinking Ricci solitons.…

We consider the magnetic Schr\"odinger operator in the unit disk with constant magnetic field of strength $b>0$ and magnetic Neumann boundary condition. If $\lambda_1(b)$ denotes its lowest eigenvalue, then we prove that $\lambda_1(b) <…

We determine accurate asymptotics for the low-lying eigenvalues of the Robin Laplacian when the Robin parameter goes to $-\infty$. The two first terms in the expansion have been obtained by K. Pankrashkin in the $2D$-case and by K.…