A boundary value problem for the wave equation.
A characterization of balls using the domain derivative.
A class of generalized integral operators.
A criterion for discrete spectra of partial differential operators
A directional compactification of the complex Fermi surface and isospectrality
A discrete Hardy-Laptev-Weidl-type inequality and associated Schrödinger-type operators.
A discreteness criterion for the spectrum of the Laplace--Beltrami operator on quasimodel manifolds.
A Two-Particle Quantum System with Zero-Range Interaction
We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.
About a non-homogeneous Hardy-inequality and its relation with the spectrum of Dirac operators
A non-homogeneous Hardy-like inequality has recently been found to be closely related to the knowledge of the lowest eigenvalue of a large class of Dirac operators in the gap of their continuous spectrum.
About a Pólya-Schiffer inequality
For simply connected planar domains with the maximal conformal radius 1 it was proven in 1954 by G. Pólya and M. Schiffer that for the eigenvalues λ of the fixed membrane for any n the following inequality holds [...] where λ(o) are the eigenvalues of the unit disk. The aim of the paper is to give a sharper version of this inequality and for the sum of all reciprocals to derive formulas which allow in some cases to calculate exactly this sum.
Alcuni risultati di teoria spettrale per l'operatore di Laplace in regioni non limitate con frontiera non regolare
An addition theorem for the manifolds with the Laplacian having discrete spectrum.
An Elliptic Boundary Value problem occurring in Magnetohydrodynamcis.
An inverse eigenvalue problem for an arbitrary multiply connected bounded region in .
An inverse eigenvalue problem for an arbitrary multiply connected bounded region: An extension to higher dimensions.
An inverse problem for a general doubly-connected bounded domain with impedance boundary conditions.
An Isoperimetric Inequality for the Principal Eigenvalue of a Periodic-Parabolic Problem.
Analyse semi-classique de l'effet tunnel
Analyse semi-classique pour l'équation de Harper
Analysis of a Population Model Structured by the Cells Molecular Content
We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak assumptions, and deduce from it the long-time convergence. The main difficulty comes from natural degeneracy of birth terms that we overcome with a regularization technique. We then extend the results to the case with several parameters and recall the link between this...