Related papers: Spectral geometry of the Steklov problem

For a given bounded domain $\Omega$ with smooth boundary in a smooth Riemannian manifold $(\mathcal{M},g)$, we show that the Poisson type upper-estimate of the heat kernel associated to the Dirichlet-to-Neumann operator, the Sobolev trace…

We prove a lower bound for the $k$-th Steklov eigenvalues in terms of an isoperimetric constant called the $k$-th Cheeger-Steklov constant in three different situations: finite spaces, measurable spaces, and Riemannian manifolds. These…

In this paper we study the asymptotic behavior of some optimal design problems related to nonlinear Steklov eigenvalues, under irregular (but diffeomorphic) perturbations of the domain.

In this article, we study the mixed Steklov--Neumann eigenvalue problem on doubly connected domains. First, we show that among all doubly connected domains in $\mathbb{R}^n$ of the form $B_{R_2}\setminus \overline{B_{R_1}}$, where $B_{R_1}$…

We consider the dependence of non-zero Steklov eigenvalues on smooth perturbations of the domain boundary. We prove that these eigenvalues are generically simple under such boundary perturbations. This result complements our previous work…

This paper is devoted to studying impedance eigenvalues (that is, eigenvalues of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic wave problem, and their potential use as target-signatures for fluid-solid…

This paper is a brief account of the Steklov eigenvalue problem on a 2-dimensional rectangular domain, and then on a 3-dimensional rectangular box. It is divided into four sections. Section 1 relies heavily on real analytic methods to show…

First we establish a weighted Reilly formula for differential forms on a smooth compact oriented Riemannian manifold with boundary. Then we give two applications of this formula when the manifold satisfies certain geometric conditions. One…

In this paper, two interesting eigenvalue comparison theorems for the first non-zero Steklov eigenvalue of the Laplacian have been established for manifolds with radial sectional curvature bounded from above. Besides, sharper bounds for the…

We consider the class of compact n-dimensional Riemannian manifolds with cylindrical boundary, Ricci curvature bounded below by a given constant and injectivity radius bounded below by a positive constant, away from the boundary. For a…

In this paper, by using the similar methods of [O. Sh. Mukhtarov and M. Kadakal, Some spectral properties of one Sturm-Liouville type problem with discontinuous weight, Siberian Mathematical Journal, 46 (2005) 681-694] we extend some…

We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of mass concentration at the boundary of a ball. We discuss the asymptotic behavior of the Neumann eigenvalues and find explicit…

We prove sharp upper and lower bounds for the nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces with boundary. The argument involves frequency function methods for harmonic functions in the interior of the surface…

We will study the generalized Steklov Robin eigensystem (with possibly matrices weights) in which the spectral parameter is both in the system and on the boundary. We prove the existence of of an increasing unbounded sequence of eigenvalues…

We justify the Weyl asymptotic formula for the eigenvalues of the Poincar\'e-Steklov spectral problem for a domain bounded by a Lipschitz surface.

We define and study the properties of Darboux-type transformations between Sturm--Liouville problems with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary…

In study of eigenvalue problems, a classical problem is the Stekloff eigenvalue problem. There are many estimates of the first non- zero Stekloff eigenvalue, including a sharp estimate on surfaces, obtained by Escobar in "The geometry of…

We study the eigenvalues of the Dirichlet-to-Neumann operator on a finite subgraph of the integer lattice Zn. We estimate the first n+1 eigenvalues using the number of vertices of the subgraph. As a corollary, we prove that the first…

We study the biharmonic Steklov eigenvalue problem on a compact Riemannian manifold $\Omega$ with smooth boundary. We give a computable, sharp lower bound of the first eigenvalue of this problem, which depends only on the dimension, a lower…

Let $M^n=[0,R)\times \mathbb{S}^{n-1}$ be an $n$-dimensional ($n\geq 2$) smooth Riemannian manifold equipped with the warped product metric $g=dr^2+h^2(r)g_{\mathbb{S}^{n-1}}$ and diffeomorphic to a Euclidean ball. Assume that $M$ has…