SDLThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.http://preprints.sissa.it:80/xmlui2018-09-19T19:09:43Z2018-09-19T19:09:43ZOn Geometric Quantum Confinement in Grushin-Like ManifoldsGallone, MatteoMichelangeli, AlessandroPozzoli, Eugeniohttp://preprints.sissa.it/handle/1963/353222018-09-19T07:05:15Z2018-09-01T00:00:00ZOn Geometric Quantum Confinement in Grushin-Like Manifolds
Gallone, Matteo; Michelangeli, Alessandro; Pozzoli, Eugenio
We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis in each fibre, thus fully characterising the regimes of presence and absence of essential self-adjointness of the associated Laplace-Beltrami operator.
16 pages
2018-09-01T00:00:00ZHydrogenoid Spectra with Central PerturbationsGallone, MatteoMichelangeli, Alessandrohttp://preprints.sissa.it/handle/1963/353212018-08-28T00:00:25Z2018-08-01T00:00:00ZHydrogenoid Spectra with Central Perturbations
Gallone, Matteo; Michelangeli, Alessandro
Through the Kreĭn-Višik-Birman extension scheme, unlike the previous
classical analysis based on von Neumann's theory, we reproduce the construction
and classification of all self-adjoint realisations of two intimately related models:
the three-dimensional hydrogenoid-like Hamiltonians with singular perturbation
supported at the centre (the nucleus), and the Schördinger operators on the halfline
with Coulomb potentials centred at the origin. These two problems are technically
equivalent, albeit sometimes treated by their own in the the literature. Based
on such scheme, we then recover the formula to determine the eigenvalues of each
self-adjoint extension, which are corrections to the non-relativistic hydrogenoid energy
levels.We discuss in which respect the Kreĭn-Višik-Birman scheme is somehow
more natural in yielding the typical boundary condition of self-adjointness at the
centre of the perturbation and in identifying the eigenvalues of each extension.
Mathematics Subject Classification (2010) 34L10 . 34L15 . 34L16 . 47B15 . 47B25 . 47N20 . 81Q10 . 81Q80
2018-08-01T00:00:00ZEnergy-dissipation balance of a smooth moving crackCaponi, MaicolLucardesi, IlariaTasso, Emanuelehttp://preprints.sissa.it/handle/1963/353202018-08-02T00:00:27Z2018-08-01T00:00:00ZEnergy-dissipation balance of a smooth moving crack
Caponi, Maicol; Lucardesi, Ilaria; Tasso, Emanuele
In this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the
result in [S. Nicaise, A.M. Sandig - J. Math. Anal. Appl., 2007] valid for straight fractures.
2018-08-01T00:00:00ZExistence and uniqueness of dynamic evolutions for a one dimensional debonding model with dampingRiva, FilippoNardini, Lorenzohttp://preprints.sissa.it/handle/1963/353192018-07-17T00:00:25Z2018-07-16T00:00:00ZExistence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping
Riva, Filippo; Nardini, Lorenzo
In this paper we analyse a one-dimensional debonding model for a thin film peeled
from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth's criterion.
2018-07-16T00:00:00Z