Related papers: Influence of the bound states in the Neumann Lapla…

In this paper we prove a sharp lower bound for the first nontrivial Neumann eigenvalue $\mu_1(\Omega)$ for the $p$-Laplace operator in a Lipschitz, bounded domain $\Omega$ in $\R^n$. Our estimate does not require any convexity assumption on…

We study the Laplacian in deformed thin (bounded or unbounded) tubes in ?$\R^3$, i.e., tubular regions along a curve $r(s)$ whose cross sections are multiplied by an appropriate deformation function $h(s)> 0$. One the main requirements on…

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…

In this paper we study the asymptotic behavior of the principal eigenvalues associated to the Pucci operator in bounded domain $\Omega$ with Neumann/Robin boundary condition i.e. $\partial_n u=\alpha u$ when $\alpha$ tends to infinity. This…

In this note we investigate spectral properties of a periodic waveguide $\Omega^\varepsilon$ ($\varepsilon$ is a small parameter) obtained from a straight strip by attaching an array of $\varepsilon$-periodically distributed identical…

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…

The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal…

Assume that $\Omega_{1}$ and $\Omega_{2}$ are two smooth bounded pseudoconvex domains in $\mathbb{C}^{2}$ that intersect (real) transversely, and that $\Omega_{1} \cap \Omega_{2}$ is a domain (i.e. is connected). If the…

We consider the waveguide modelled by a $n$-dimensional infinite tube. The operator we study is the Dirichlet Laplacian perturbed by two distant perturbations. The perturbations are described by arbitrary abstract operators ''localized'' in…

This paper is devoted to the spectral analysis of the Laplacian with constant magnetic field on a cone of aperture $\alpha$ and Neumann boundary condition. We analyze the influence of the orientation of the magnetic field. In particular,…

Let $\Omega$ be an open, bounded domain in the plane with connected and smooth boundary, and $\omega$ an eigenfunction of the Neumann Laplacian corresponding to some Neumann eigenvalue $\mu > 0$. If the boundary value of $\omega$ is a…

We consider two-dimensional waveguide with a rectangular obstacle symmetric about the axis of the waveguie. We study the behaviour of the Neumann eigenvalues located below the first threshold when the sides of the obstacle approach the…

We study high energy resonances for the operator $-\Delta_{V,\partial\Omega}:=-\Delta+\delta_{\partial\Omega}\otimes V $ when $V$ has strong frequency dependence. The operator $-\Delta_{V,\partial\Omega}$ is a Hamiltonian used to model both…

With a densely defined symmetric semi-bounded operator of nonzero defect indexes $L_0$ in a separable Hilbert space ${\cal H}$ we associate a topological space $\Omega_{L_0}$ ({\it wave spectrum}) constructed from the reachable sets of a…

For a bounded corner domain $\Omega$, we consider the Robin Laplacian in $\Omega$ with large Robin parameter. Exploiting multiscale analysis and a recursive procedure, we have a precise description of the mechanism giving the ground state…

We consider the Laplace operator in a thin three dimensional tube with a Robin type condition on its boundary and study, asymptotically, the spectrum of such operator as the diameter of the tube's cross section becomes infinitesimal. In…

We analyze the behavior of the eigenvalues and eigenfunctions of the Laplace operator with homogeneous Neumann boundary conditions when the domain is perturbed. We focus on exterior perturbations of the domain, that is, the limit domain is…

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…

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…

Let $\Omega\subset\mathbb{R}^N$, $N\geq 1$, be an open bounded connected set. We consider the indefinite weighted eigenvalue problem $-\Delta u =\lambda m u$ in $\Omega$ with $\lambda \in \mathbb{R}$, $m\in L^\infty(\Omega)$ and with…