Related papers: Two-phase eigenvalue problem on thin domains with …
We study the variation of the Neumann eigenvalues of the $p$-Laplace operator under quasiconformal perturbations of space domains. This study allows to obtain lower estimates of the Neumann eigenvalues in fractal type domains. The suggested…
We study the asymptotic behaviour of the eigenvalues of the Laplace-Beltrami operator on a compact hypersurface in \mathds{R}^{n+1} as it is flattened into a singular double-sided flat hypersurface. We show that the limit spectral problem…
It is natural to consider continuous dependence of the $n$-th eigenvalue on $d$-dimensional ($d\geq2$) Sturm-Liouville problems after the results on $1$-dimensional case by Kong, Wu and Zettl [14]. In this paper, we find all the boundary…
We exhibit some large variations solutions of the Landau-Lifschitz equations as the exchange coefficient ε^2 tends to zero. These solutions are described by some asymptotic expansions which involve some internals layers by means of…
The eigenvalue problem for the dressed bound-state of unstable multilevel systems is examined both outside and inside the continuum, based on the N-level Friedrichs model which describes the couplings between the discrete levels and the…
Hyperbolic systems of the first and higher-order partial differential equations appear in many multiphysics problems. We will be dealing with a wave propagation problem in a piece-wise homogeneous medium. Mathematically, the problem is…
We consider the nonlinear eigenvalue problem, with Dirichlet boundary condition, for a class of very degenerate elliptic operators, with the aim to show that, at least for square type domains having fixed volume, the symmetry of the domain…
We study the existence of Neumann eigenfunctions which do not change sign on the boundary of some special domains. We show that eigenfunctions which are strictly positive on the boundary exist on regular polygons with at least 5 sides,…
The present work deals with the resolution of the Poisson equation in a bounded domain made of a thin and periodic layer of finite length placed into a homogeneous medium. We provide and justify a high order asymptotic expansion which takes…
We consider a nonlinear eigenvalue problem under Robin boundary conditions in a domain with (possibly noncompact) smooth boundary. The problem involves a weighted p-Laplacian operator and subcritical nonlinearities satisfying…
This article investigates how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain in the case when the domains involved are of class $C^1$. We consider the Laplacian and use results developed previously for…
Given a convex domain and its convex sub-domain we prove a variant of domain monotonicity for the Neumann eigenvalues of the Laplacian. As an application of our method we also obtain an upper bound for Neumann eigenvalues of the Laplacian…
We investigate asymptotic behavior of solutions for nonlocal elliptic boundary value problems in plane angles and in ${\mathbb R}^2\backslash\{0\}$. Such problems arise as model ones when studying asymptotics of solutions for nonlocal…
The aim of this article is to analyze numerical schemes using two-layer neural networks withinfinite width for the resolution of high-dimensional Schr{\"o}dinger eigenvalue problems with smoothinteraction potentials and Neumann boundary…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
Let $\Omega$ be a bounded domain in $\mathbb R^2$ with smooth boundary $\partial\Omega$, and let $\omega_h$ be the set of points in $\Omega$ whose distance from the boundary is smaller than $h$. We prove that the eigenvalues of the…
We study periodic homogenization problems for second-order pde in half-space type domains with Neumann boundary conditions. In particular, we are interested in "singular problems" for which it is necessary to determine both the homogenized…
We address the problem of splitting of eigenvalues of the Neumann Laplacian under singular domain perturbations. We consider a domain perturbed by the excision of a small spherical hole shrinking to an interior point. Our main result…
We investigate dynamics of large scale and slow deformations of layered structures. Starting from the respective model equations for a non-conserved system, a conserved system and a binary fluid, we derive the interface equations which are…
We consider the linear damped wave equation on finite metric graphs and analyse its spectral properties with an emphasis on the asymptotic behaviour of eigenvalues. In the case of equilateral graphs and standard coupling conditions we show…