Related papers: Spectral Stability of the $\bar\partial-$Neumann L…
We study spectral stability of the $\bar\partial$-Neumann Laplacian on a bounded domain in $\mathbb{C}^n$ when the underlying domain is perturbed. In particular, we establish upper semi-continuity properties for the variational eigenvalues…
In this paper we establish new quantitative stability estimates with respect to domain perturbations for all the eigenvalues of both the Neumann and the Dirichlet Laplacian. Our main results follow from an abstract lemma stating that it is…
We study spectral stability estimates of elliptic operators in divergence form $-\textrm{div} [A(w) \nabla g(w)]$ with the Neumann boundary condition in non-Lipschitz domains $\Omega \subset \mathbb C$. The suggested method is based on…
We present an analysis of the stability spectrum of all stationary elliptic-type solutions to the focusing Nonlinear Schr\"{o}dinger equation (NLS). An analytical expression for the spectrum is given. From this expression, various…
We study the inverse problem of identifying a periodic potential perturbation of the Dirichlet Laplacian acting in an infinite cylindrical domain, whose cross section is assumed to be bounded. We prove log-log stable determination of the…
We study the eigenvalue problem for the Neumann-Laplace operator in conformal regular planar domains $\Omega\subset\mathbb{C}$. Conformal regular domains support the Poincar\'e inequality and this allows us to estimate the variation of the…
We examine the stability of the elliptic solutions of the focusing nonlinear Schr\"odinger equation (NLS) with respect to subharmonic perturbations. Using the integrability of NLS, we discuss the spectral stability of the elliptic…
We establish sharp regularity and Fredholm theorems for the \bar{\partial}_b-Neumann problem on domains satisfying some non-generic geometric conditions. We use these domains to construct explicit examples of bad behaviour of the Kohn…
We present an analysis of the stability spectrum for all stationary periodic solutions to the sine-Gordon equation. An analytical expression for the spectrum is given. From this expression, various quantitative and qualitative results about…
This paper deals with quantitative spectral stability for compact operators acting on $L^2(X,m)$, where $(X,m)$ is a measure space. Under fairly general assumptions, we provide a characterization of the dominant term of the asymptotic…
We study the $\bar\partial$-Neumann Laplacian from spectral theoretic perspectives. In particular, we show how pseudoconvexity of a bounded domain is characterized by positivity of the $\bar\partial$-Neumann Laplacian.
In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology.
We study the behaviour of eigenvalues, below the bottom of the essential spectrum, of the Laplacian under finite Riemannian coverings of complete and connected Riemannian manifolds. We define spectral stability and instability of such…
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 study the Neumann Laplacian $-\Delta^N$ restricted to a periodic waveguide. In this situation its spectrum $\sigma(-\Delta^N)$ presents a band structure. Our goal and strategy is to get spectral information from an analysis of the…
We consider Dirac operators on the half-line, subject to generalised infinite-mass boundary conditions. We derive sufficient conditions which guarantee the stability of the spectrum against possibly non-self-adjoint potential perturbations…
We prove that the $\bar\partial$-Neumann solution operator is locally regular in a domain which has compactness estimates, is of finite type outside a curve transversal to the CR directions and for which the holomorphic tangential…
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…
This paper treats subelliptic estimates for the $\bar{\partial}$-Neumann problem on a class of domains known as regular coordinate domains. Our main result is that the largest subelliptic gain for a regular coordinate domain is bounded…
In this work we analyze the behavior of the spectrum of the peridynamic fractional $p$-Laplacian, $(-\Delta_p)_{\delta}^s$, under the limit process $\delta\to0^+$ or $\delta\to+\infty$. We prove spectral convergence to the classical…