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In the present paper, we study the variational properties of Steklov transmission eigenvalues, which can be seen as eigenvalues of the sum of two Dirichlet-to-Neumann operators on two different sides of a given curve contained in a surface.…

Spectral Theory · Mathematics 2025-09-30 Mikhail Karpukhin , Alain Didier Noutchegueme

We consider time-harmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to sign-changing permittivity and/or permeability. Previously meshing…

Numerical Analysis · Mathematics 2021-04-20 Martin Halla

This is a continuation of our previous work arXiv:1601.05617 on trace and inverse trace of Steklov eigenvalues. More new inequalities for the trace and inverse trace of Steklov eigenvalues are obtained.

Differential Geometry · Mathematics 2016-09-02 Yongjie Shi , Chengjie Yu

We investigate the Steklov eigenvalue problem in an exterior Euclidean domain. First, we present several formulations of this problem and establish the equivalences between them. Next, we examine various properties of the exterior Steklov…

Spectral Theory · Mathematics 2025-12-05 Lukas Bundrock , Alexandre Girouard , Denis S. Grebenkov , Michael Levitin , Iosif Polterovich

This paper is concerned with the inverse scattering and the transmission eigenvalues for anisotropic periodic layers. For the inverse scattering problem, we study the Factorization method for shape reconstruction of the periodic layers from…

Analysis of PDEs · Mathematics 2020-01-10 Isaac Harris , Dinh-Liem Nguyen , Jonathan Sands , Trung Truong

We propose a multigrid correction scheme to solve a new Steklov eigenvalue problem in inverse scattering. With this scheme, solving an eigenvalue problem in a fine finite element space is reduced to solve a series of boundary value problems…

Numerical Analysis · Mathematics 2018-06-18 Yu Zhang , Hai Bi , Yidu Yang

In this paper, we consider a new transmission eigenvalue problem derived from the scattering by a clamped cavity in a thin elastic material. Scattering in a thin elastic material can be modeled by the Kirchhoff--Love infinite plate problem.…

Analysis of PDEs · Mathematics 2025-02-04 Isaac Harris , Heejin Lee , Andreas Kleefeld

We study Markov processes associated with stochastic differential equations, whose non-linearities are gradients of convex functionals. We prove a general result of existence of such Markov processes and a priori estimates on the transition…

Probability · Mathematics 2007-05-23 Luigi Ambrosio , Giuseppe Savare , Lorenzo Zambotti

Eigenvalues of stochastic matrices have been studied from two complementary perspectives. The individual eigenvalues are characterised through the well-established Karpelevich regions. The spectrum as a whole has also been analysed,…

Spectral Theory · Mathematics 2025-12-19 Brando Vagenende , Brecht Verbeken , Marie-Anne Guerry

This paper investigates the asymptotic behavior of the eigenvalues of the biharmonic operator on a thin set with Steklov boundary condition. The thin set is taken to be a tubular neighborhood of a planar smooth domain. We show that, as the…

Analysis of PDEs · Mathematics 2026-03-03 Bauyrzhan Derbissaly , Nurbek kakharman

In this paper, we study the so-called clamped transmission eigenvalue problem. This is a new transmission eigenvalue problem that is derived from the scattering of an impenetrable clamped obstacle in a thin elastic plate. The scattering…

Analysis of PDEs · Mathematics 2025-11-21 Isaac Harris , Andreas Kleefeld , Heejin Lee

We consider the scattering problem on locally perturbed periodic penetrable dielectric layers, which is formulated in terms of the full vector-valued time-harmonic Maxwell's equations. The right-hand side is not assumed to be periodic. At…

Analysis of PDEs · Mathematics 2019-08-23 Alexander Konschin

In this paper, we consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which…

Numerical Analysis · Mathematics 2016-08-24 Fang Zeng , Jiguang Sun , Liwei Xu

In this paper we study microlocal singularities of solutions to Schrodinger equations on scattering manifolds, i.e., noncompact Riemannian manifolds with asymptotically conic ends. We characterize the wave front set of the solutions in…

Analysis of PDEs · Mathematics 2007-11-22 Kenichi Ito , Shu Nakamura

We derive an analytical expression for the scattering of a scalar wave from a perfectly conducting self-affine one dimensional surface in the framework of the Kirchhoff approximation. We show that most of the results can be recovered via a…

Other Condensed Matter · Physics 2009-11-10 Ingve Simonsen , Damien Vandembroucq , Stephane Roux

We investigate a class of parametric elliptic eigenvalue problems with homogeneous essential boundary conditions where the coefficients (and hence the solution $u$) may depend on a parameter $y$. For the efficient approximate evaluation of…

Numerical Analysis · Mathematics 2024-05-17 Alexey Chernov , Tung Le

We study the eigenvalue problem for some special class of anti-triangular matrices. Though the eigenvalue problem is quite classical, as far as we know, almost nothing is known about properties of eigenvalues for anti-triangular matrices.…

Rings and Algebras · Mathematics 2014-03-27 Hiroyuki Ochiai , Makiko Sasada , Tomoyuki Shirai , Takashi Tsuboi

We find some new results regarding the existence, uniqueness, boundedness, stability and attractivity of the solutions of a class of initial-boundary-value problems characterized by a quasi-linear third order equation which may have…

Mathematical Physics · Physics 2012-09-28 Armando D'Anna , Gaetano Fiore

Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…

Optics · Physics 2009-11-10 Diana C. Skigin

In this paper, we consider an interior transmission eigenvalue (ITE) problem on some compact $C^{\infty }$-Riemannian manifolds with a common smooth boundary. In particular, these manifolds may have different topologies, but we impose some…

Spectral Theory · Mathematics 2019-05-27 Hisashi Morioka , Naotaka Shoji