Related papers: Symmetry and uniqueness for a hinged plate problem…
We investigate a two-dimensional transmission model consisting of a wave equation and a Kirchhoff plate equation with dynamical boundary controls under geometric conditions. The two equations are coupled through transmission conditions…
The aim of this paper is to study existence results for a singular problem involving the $p$-biharmonic operator and the Hardy potential. More precisely, by combining monotonicity arguments with the variational method, the existence of…
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.…
This paper is concerned with the existence and qualitative properties of positive ground state solutions for the planar Schr\"odinger-Newton equation on the disc. First, we prove the existence and radial symmetry of all the positive ground…
In this paper we prove the uniqueness and radial symmetry of minimizers for variational problems that model several phenomena. The uniqueness is a consequence of the convexity of the functional. The main technique is Fourier transform of…
In this paper we prove radial symmetry for solutions to a free boundary problem with a singular right hand side, in both elliptic and parabolic regime. More exactly, in the unit ball $B_1$ we consider a solution to the fully nonlinear…
This article is devoted to the study of spectral optimisation for inhomogeneous plates. In particular, we optimise the first eigenvalue of a vibrating plate with respect to its thickness and/or density. Our result is threefold. First, we…
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…
We obtain the radial symmetry of the solution to a partially overdetermined boundary value problem in a convex cone in space forms by using the maximum principle for a suitable subharmonic function $P$ and integral identities. In dimension…
We consider a class of weighted harmonic functions in the open upper half-plane known as $\alpha$-harmonic functions. Of particular interest is the uniqueness problem for such functions subject to a vanishing Dirichlet boundary value on the…
We present a new isogeometric method for the discretization of the Reissner-Mindlin plate bending problem. The proposed scheme follows a recent theoretical framework that makes possible to construct a space of smooth discrete deflections…
A plate is rigid if its admissible displacement fields inducing vanishing two-dimensional strain tensors must vanish. We prove that the nonlinear model of Kirchhoff-Love for such a plate has a solution for any applied forces and boundary…
We consider a thin and narrow rectangular plate where the two short edges are hinged whereas the two long edges are free. This plate aims to represent the deck of a bridge, either a footbridge or a suspension bridge. We study a nonlocal…
The problem of covering a region of the plane with a fixed number of minimum-radius identical balls is studied in the present work. An explicit construction of bi-Lipschitz mappings is provided to model small perturbations of the union of…
We consider ground states solutions $u \in H^2(\mathbb{R}^N)$ of biharmonic (fourth-order) nonlinear Schr\"odinger equations of the form $$ \Delta^2 u + 2a \Delta u + b u - |u|^{p-2} u = 0 \quad \mbox{in $\mathbb{R}^N$} $$ with positive…
We introduce a notion of homogeneous topological order, which is obeyed by most, if not all, known examples of topological order including fracton phases on quantum spins (qudits). The notion is a condition on the ground state subspace,…
We derive a simple criterion that ensures uniqueness, Lipschitz stability and global convergence of Newton's method for the finite dimensional zero-finding problem of a continuously differentiable, pointwise convex and monotonic function.…
This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…
We consider the eigenvalue problem for the Reissner-Mindlin system arising in the study of the free vibration modes of an elastic clamped plate. We provide quantitative estimates for the variation of the eigenvalues upon variation of the…
We consider the two-dimensional Kirchhoff-Love plate equation in the context of elasticity modeling the stresses and deformations in thin plates subjected to forces and moments. We establish global recovery of the material parameters like…