Related papers: On the Robin spectrum for the hemisphere

Consider a bounded domain with the Dirichlet condition on a part of the boundary and the Neumann condition on its complement. Does the spectrum of the Laplacian determine uniquely which condition is imposed on which part? We present some…

We study a class of delta-like perturbations of the Laplacian on the half-line, characterized by Robin boundary conditions at the origin. Using the formalism of nonstandard analysis, we derive a simple connection with a suitable family of…

We consider spectral problems for Laplace operator in 3D rod structures with a small cross section of diameter $O(\varepsilon)$, $\varepsilon$ being a positive parameter. The boundary conditions are Dirichlet (Neumann, respectively) on the…

For $\alpha\in(0,\pi)$, let $U_\alpha$ denote the infinite planar sector of opening $2\alpha$, \[ U_\alpha=\big\{ (x_1,x_2)\in\mathbb R^2: \big|\arg(x_1+ix_2) \big|<\alpha \big\}, \] and $T^\gamma_\alpha$ be the Laplacian in…

Let $\Omega\subset\mathbb{R}^n$ be a bounded domain. We perturb it to a domain $\Omega^\varepsilon$ attaching a family of small protuberances with "room-and-passage"-like geometry ($\varepsilon>0$ is a small parameter). Peculiar spectral…

We study the behaviour, as $p \to +\infty$, of the second eigenvalues of the $p$-Laplacian with Robin boundary conditions and the limit of the associated eigenfunctions. We prove that, up to some regularity of the set, the limit of the…

We study convergence modes as well as their respective rates for the resolvent difference of Robin and Dirichlet Laplacian on bounded smooth domains in the large coupling limit. Asymptotic expansions for the resolvent, the eigenprojections…

In this paper, we investigate the existence and uniqueness of solutions for the following model problem, involving singularities and inhomogeneous Robin boundary conditions \begin{equation*} \left\{ \begin{array}{ll}…

In this work we analyse the convergence of solutions of the Poisson equation with Neumann boundary conditions in a thin domain with highly oscillatory behavior $\mathcal{U}^\varepsilon$ contained in the sphere $\mathbb{S}^2$. Using the…

We consider a compact Riemannian manifold with a Hermitian line bundle whose curvature is non degenerate. Under a general condition, the Laplacian acting on high tensor powers of the bundle exhibits gaps and clusters of eigenvalues. We…

We consider the Laplacian in a strip $\mathbb{R}\times (0,d)$ with the boundary condition which is Dirichlet except at the segment of a length $2a$ of one of the boundaries where it is switched to Neumann. This operator is known to have a…

We study asymptotic distribution of eigenvalues of the Laplacian on a bounded domain in $ \R^n$. Our main results include an explicit remainder estimate in the Weyl formula for the Dirichlet Laplacian on an arbitrary bounded domain,…

Motivated by the study of high energy Steklov eigenfunctions, we examine the semi-classical Robin Laplacian. In the two dimensional situation, we determine an effective operator describing the asymptotic distribution of the negative…

We consider the first Robin eigenvalue $\l_p(M,\a)$ for the $p$-Laplacian on a compact Riemannian manifold $M$ with nonempty smooth boundary, with $\a \in \R$ being the Robin parameter. Firstly, we prove eigenvalue comparison theorems of…

In this paper we deal with spectral optimization for the Robin Laplacian on a family of planar domains admitting parallel coordinates, namely a fixed-width strip built over a smooth closed curve and the exterior of a convex set with a…

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…

This article is the continuation of our first work on the determination of the cases where there is equality in Courant's Nodal Domain theorem in the case of a Robin boundary condition (with Robin parameter $h$). For the square, our first…

In this note we investigate the asymptotic behaviour of the $s$-numbers of the resolvent difference of two generalized self-adjoint, maximal dissipative or maximal accumulative Robin Laplacians on a bounded domain $\Omega$ with smooth…

The second eigenvalue of the Robin Laplacian is shown to be maximal for a spherical cap among simply connected Jordan domains on the 2-sphere, for substantial intervals of positive and negative Robin parameters and areas. Geodesic disks in…

Existence and global regularity results for boundary-value problems of Robin type for harmonic and polyharmonic functions in $n$-dimensional half-spaces are offered. The Robin condition on the normal derivative on the boundary of the…