Related papers: Steklov eigenvalues of nearly circular area-normal…

Motivated by the connection between the first eigenvalue of the Dirichlet-Laplacian and the torsional rigidity, the aim of this paper is to find a physically coherent and mathematically interesting new concept for boundary torsional…

We study upper bounds for the first non-zero eigenvalue of the Steklov problem defined on finite graphs with boundary. For finite graphs with boundary included in a Cayley graph associated to a group of polynomial growth, we give an upper…

Using expander graphs, we construct a sequence of smooth compact surfaces with boundary of perimeter N, and with the first non-zero Steklov eigenvalue uniformly bounded away from zero. This answers a question which was raised in [9]. The…

We study oscillations in the eigenfunctions for a fractional Schr\"odinger operator on the real line. An argument in the spirit of Courant's nodal domain theorem applies to an associated local problem in the upper half plane and provides a…

We study the nodal set of the Steklov eigenfunctions on the boundary of a smooth bounded domain in $\mathbb{R}^n$ - the eigenfunctions of the Dirichlet-to-Neumann map. Under the assumption that the domain $\Omega$ is $C^2$, we prove a…

We analyse the asymptotic behaviour of the eigenvalues and eigenvectors of a Steklov problem in a dumbbell domain consisting of two Lipschitz sets connected by a thin tube with vanishing width. All the eigenvalues are collapsing to zero,…

We investigate the eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We obtain universal bounds for the $k$th eigenvalue in terms of the lower eigenvalues independently of the…

We study a new link between the Steklov and Neumann eigenvalues of domains in Euclidean space. This is obtained through an homogenisation limit of the Steklov problem on a periodically perforated domain, converging to a family of eigenvalue…

We study the Steklov eigenvalue problem for the $\infty-$orthotropic Laplace operator defined on convex sets of $\mathbb{R}^N$, with $N\geq2$, considering the limit for $p\to+\infty$ of the Steklov problem for the $p-$orthotropic Laplacian.…

We prove two explicit bounds for the multiplicities of Steklov eigenvalues $\sigma_k$ on compact surfaces with boundary. One of the bounds depends only on the genus of a surface and the index $k$ of an eigenvalue, while the other depends as…

In this paper, we study the computational question of whether the Steklov spectrum of smooth simply connected planar domains can be approximated accurately by a boundary-only formulation based on harmonic conjugation. For the unit disk, the…

The inverse problem of recovering a smooth simply connected multisheet planar domain from its Steklov spectrum is equivalent to the problem of determination, up to a gauge transform, of a smooth positive function $a$ on the unit circle from…

We study the maximal Steklov eigenvalues of trees with given number of boundary vertices and total number of vertices. Trees can be regarded as discrete analogue of Hadamard manifolds, namely simply-connected Riemannian manifolds of…

Consider a compact Riemannian manifold with boundary. In this short note we prove that under certain positive curvature assumptions on the manifold and its boundary the Steklov eigenvalues of the manifold are controlled by the Laplace…

We consider the Steklov eigenvalue problem on a compact pinched negatively curved manifold $M$ of dimension at least three with totally geodesic boundaries. We obtain a geometric lower bound for the first nonzero Steklov eigenvalue in terms…

This paper studies eigenvalues of the buckling problem of arbitrary order on bounded domains in Euclidean spaces and spheres. We prove universal bounds for the k-th eigenvalue in terms of the lower ones independent of the domains. Our…

We consider the Laplace operator with Dirichlet boundary conditions on a domain in R^d and study the effect that performing a scaling in one direction has on the eigenvalues and corresponding eigenfunctions as a function of the scaling…

In this article, we investigate the weighted Steklov eigenvalue problem and the weighted Schr\"odinger--Steklov eigenvalue problem in outward cuspidal domains. We prove the solvability of these spectral problems in both linear and…

In this paper, we obtain some new estimates for the trace and inverse trace of Steklov eigenvalues. The estimates generalize some previous results of Hersch-Payne-Schiffer , Brock}, Raulot-Savo and Dittmar.

We give improvements of estimates of invariant metrics in the normal direction on strictly pseudoconvex domains. Specifically we will give the second term in the expansion of the metrics. This depends on an improved localisation result and…