Related papers: Generalized spectrum of Steklov-Robin problem for …
We introduce the biharmonic Steklov problem on differential forms by considering suitable boundary conditions. We characterize its smallest eigenvalue and prove elementary properties of the spectrum. We obtain various estimates for the…
In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the…
Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…
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…
We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic…
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 consider how the geometry and topology of a compact $n$-dimensional Riemannian orbifold with boundary relates to its Steklov spectrum. In two dimensions, motivated by work of A. Girouard, L. Parnovski, I. Polterovich and D. Sher in the…
In this article I will review some basic results on elliptic boundary value problems with applications to General Relativity.
In this paper, we consider the numerical approximation of the Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering problem is for an inhomogeneous isotropic medium. These eigenvalues have been…
The asymptotic behavior of second order self-adjoint elliptic Steklov eigenvalue problems with periodic rapidly oscillating coefficients and with indefinite (sign-changing) density function is investigated in periodically perforated…
This paper develops the notion and properties of the generalized principal eigenvalue for an elliptic system coupling an equation in a plane with one on a line in this plane, together with boundary conditions that express exchanges taking…
A recent area of interest is the development and study of eigenvalue problems arising in scattering theory that may provide potential target signatures for use in nondestructive testing of materials. We consider a generalization of the…
The spectrum of Markov generators encodes physical information beyond simple decay and oscillation, which reflects irreversibility and governs the structure of correlation functions. In this work, we prove an ellipse theorem that provides a…
Recently, their has been development of an abstract approach to the Robin--Robin method, enabling the treatment of linear and nonlinear elliptic and parabolic equations on Lipschitz domains within one framework. However, previously this…
We report on a general purpose method for the scalar Stefan problem inspired by the standard boundary updating method used in several existence proofs. By suitably modifying it we can solve numerically any kind of Stefan problem. We present…
In this paper the first and second domain variation for functionals related to elliptic boundary and eigenvalue problems with Robin boundary conditions is computed. Minimality and maximality properties of the ball among nearly circular…
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…
We are concerned with the solvability of linear second order elliptic partial differential equations with nonlinear boundary conditions at resonance, in which the nonlinear boundary conditions perturbation is not necessarily required to…
We study the spectral problem associated with the equation governing the small transverse motions of a viscoelastic tube of finite length conveying an ideal fluid. The boundary conditions considered are of general form, accounting for a…
We study bounds on the Riesz means of the mixed Steklov-Neumann and Steklov-Dirichlet eigenvalue problem on a bounded domain $\Omega$ in $\mathbb{R}^n$. The Steklov-Neumann eigenvalue problem is also called the sloshing problem. We obtain…