SISSA Preprints
http://preprints.sissa.it:8080/xmlui/handle/1963/35281
SISSA authors' not-referred manuscripts of the research outputThu, 26 May 2022 23:00:35 GMT2022-05-26T23:00:35ZContinuity of some non-local functionals with respect to a convergence of the underlying measures
http://preprints.sissa.it:8080/xmlui/handle/1963/35443
Continuity of some non-local functionals with respect to a convergence of the underlying measures
Braides, Andrea; Dal Maso, Gianni
We study some non-local functionals on the Sobolev space W1,p0(Ω) involving a
double integral on Ω × Ω with respect to a measure µ. We introduce a suitable notion
of convergence of measures on product spaces which implies a stability property in the
sense of Γ-convergence of the corresponding functionals.
Preprint SISSA 8/2022/MATE
Mon, 04 Apr 2022 00:00:00 GMThttp://preprints.sissa.it:8080/xmlui/handle/1963/354432022-04-04T00:00:00ZAsymptotic behavior of the dirichlet energy on poisson point clouds
http://preprints.sissa.it:8080/xmlui/handle/1963/35442
Asymptotic behavior of the dirichlet energy on poisson point clouds
Braides, andrea; Caroccia, Marco
We prove that quadratic pair interactions for functions defined on planar Poisson
clouds and taking into account pairs of sites of distance up to a certain (large-enough) threshold can be almost surely approximated by the multiple of the Dirichlet energy by a deterministic constant. This is achieved by scaling the Poisson cloud and the corresponding energies and computing a compact discrete-to-continuum limit. In order to avoid the effect of exceptional regions of the Poisson cloud, with an accumulation of sites or with ‘disconnected’ sites, a suitable ‘coarse-grained’ notion of convergence of functions defined on scaled Poisson clouds must be given.
SISSA 06/2022/MATE
Wed, 23 Mar 2022 00:00:00 GMThttp://preprints.sissa.it:8080/xmlui/handle/1963/354422022-03-23T00:00:00ZOn the Dirichlet problem associated to bounded perturbations of positively-(p, q)-homogeneous Hamiltonian systems
http://preprints.sissa.it:8080/xmlui/handle/1963/35441
On the Dirichlet problem associated to bounded perturbations of positively-(p, q)-homogeneous Hamiltonian systems
Fonda, Alessandro; Klun, Giuliano; Obersnel, Franco; Sfecci, Andrea
The existence of solutions for the Dirichlet problem associated to
bounded perturbations of positively-(p, q)-homogeneous Hamiltonian sys tems is considered both in nonresonant and resonant situations. In order
to deal with the resonant case, the existence of a couple of lower and up per solutions is assumed. Both the well-ordered and the non-well-ordered
cases are analysed. The proof is based on phase-plane analysis and topo logical degree theory
SISSA 03/2022/MATE
Mon, 21 Feb 2022 00:00:00 GMThttp://preprints.sissa.it:8080/xmlui/handle/1963/354412022-02-21T00:00:00ZControllability of the Schrodinger Equation via Intersection of Eigenvalues
http://preprints.sissa.it:8080/xmlui/handle/1963/35440
Controllability of the Schrodinger Equation via Intersection of Eigenvalues
Adami, R.; Boscain, U.
We introduce two models of controlled infinite
dimensional quantum system whose Hamiltonian operator has
a purely discrete spectrum. For any couple of eigenstates we
construct a path in the space of controls that approximately
steers the system from one eigenstate to the other. To this
purpose we use the adiabatic theory for quantum systems, and
therefore the strategy requires large times.
Sat, 01 Jan 2005 00:00:00 GMThttp://preprints.sissa.it:8080/xmlui/handle/1963/354402005-01-01T00:00:00Z