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We are interested in the spectrum of the Dirichlet Laplacian in thin broken strips with angle $\alpha$. Playing with symmetries, this leads us to investigate spectral problems for the Laplace operator with mixed boundary conditions in…
We present a semi-analytical approach to compute quasi-guided elastic wave modes in horizontally layered structures radiating into unbounded fluid or solid media. This problem is of relevance, e.g., for the simulation of guided ultrasound…
We construct the asymptotic approximation to the first eigenvalue and corresponding eigensolution of Laplace's operator inside a domain containing a cloud of small rigid inclusions. The separation of the small inclusions is characterised by…
In this paper we consider singular timelike spherical hypersurfaces embedded in a $D$-dimensional spherically symmetric bulk spacetime which is an electrovacuum solution of Einstein equations with cosmological constant. We analyse the…
It is well known that the usual mixed method for solving the biharmonic eigenvalue problem by decomposing the operator into two Laplacians may generate spurious eigenvalues on non-convex domains. To overcome this difficulty, we adopt a…
The efficiency of several first-order numerical schemes for two-layer shallow water equations are evaluated in this paper by considering different eigenvalue solutions. Specifically, the accuracy and computational cost of numerical,…
We present a generalization of the black hole solution with spherical symmetry already known in the literature for $N$-dimensional $F(R)$ gravity with a conformally invariant Maxwell field and constant scalar curvature $R$. This solution…
In this paper, we investigate a class of nonlinear eigenvalue problems resulting from quantum physics. We first prove that the eigenfunction cannot be a polynomial on any open set, which may be reviewed as a refinement of the classic unique…
This paper focuses on the study of Sturm-Liouville eigenvalue problems. In the classical Chebyshev collocation method, the Sturm-Liouville problem is discretized to a generalized eigenvalue problem where the functions represent interpolants…
Here, we present a least-squares based spectral element formulation for one-dimensional eigenvalue problems with interface conditions. First we develop the method for without interface case, then we extend it to interface case. Convergence…
This paper solves the open problem of the simplicity of the second Dirichlet eigenvalue for nearly equilateral triangles, offering a complete solution to Conjecture 6.47 posed by R. Laugesen and B. Siudeja in A. Henrot's book ``Shape…
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.…
In the framework of the conjectured duality relation between large $N$ gauge theory and supergravity the spectra of masses in large $N$ gauge theory can be determined by solving certain eigenvalue problems in supergravity. In this paper we…
We argue that the standard classification of isometric deformations into infinitesimal v.s. finite is inadequate for the study of compliant shell mechanisms. Indeed, many compliant shells, particularly ones that are periodically corrugated,…
The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the…
When pushed out of a syringe, polymer solutions form droplets attached by long and slender cylindrical filaments whose diameter decreases exponentially with time before eventually breaking. In the last stages of this process, a striking…
In this paper we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the…
In this paper, we study the existence and uniqueness of solutions to the weighted eigenvalue problem for $k$-Hessian equation. To achieve this, we establish the uniform a priori estimates for gradient and second derivatives of solutions to…
We revisit the $k$-Hessian eigenvalue problem on a smooth, bounded, $(k-1)$-convex domain in $\mathbb R^n$. First, we obtain a spectral characterization of the $k$-Hessian eigenvalue as the infimum of the first eigenvalues of linear…
This paper studies minimizing solutions to a two dimensional Allen-Cahn system on the upper half plane, subject to Dirichlet boundary conditions, \begin{equation*} \Delta u-\nabla_u W(u)=0, \quad u: \mathbb{R}_+^2\to \mathbb{R}^2,\ u=u_0…