SISSA PreprintsThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.http://preprints.sissa.it:80/xmlui2019-03-21T15:40:27Z2019-03-21T15:40:27ZAn asymptotic description of Noether-Lefschetz components in toric varietiesBruzzo, UgoMontoya, William D.http://preprints.sissa.it:8180/xmlui/handle/1963/353312019-03-21T01:03:35Z2019-03-19T00:00:00ZAn asymptotic description of Noether-Lefschetz components in toric varieties
Bruzzo, Ugo; Montoya, William D.
We extend the definition of Noether-Leschetz components to quasi-smooth hyper- surfaces in a projective toric variety PΣ2k+1 having orbifold singularities, and prove that asymptoticaly the components whose codimension is bounded from above are made of hy- persurfaces containing a small degree k-dimensional subvariety. As a corollary we get an asymptotic characterization of the components with small codimension, generalizing the work of Otwinowska for P2k+1 = P2k+1 and Green and Voisin for P2k+1 = P3. Some tools that are developed in the paper are a generalization of Macaulay’s theorem for Fano, irreducible normal varieties with rational singularieties, satisfying a suitable additional condition, and an extension of the notion of Gorenstein ideal for normal varieties with finetely generated Cox ring.
2019-03-19T00:00:00ZOn the topological degree of planar maps avoiding normal conesFonda, AlessandroKlun, Giulianohttp://preprints.sissa.it:8180/xmlui/handle/1963/353302019-03-21T01:03:03Z2019-03-07T00:00:00ZOn the topological degree of planar maps avoiding normal cones
Fonda, Alessandro; Klun, Giuliano
The classical Poincaré–Bohl theorem provides the exis-tence of a zero for a function avoiding external rays. When the do-main is convex, the same holds true when avoiding normal cones. We consider here the possibility of dealing with nonconvex sets having in-ward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be di˙erent from ±1.
2019-03-07T00:00:00ZA continuous dependence result for a dynamic debonding model in dimension oneRiva, Filippohttp://preprints.sissa.it:8180/xmlui/handle/1963/353292019-03-21T01:03:05Z2019-03-07T00:00:00ZA continuous dependence result for a dynamic debonding model in dimension one
Riva, Filippo
In this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin ﬁlm peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griﬃth’s criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to diﬀerent natural topologies.
2019-03-07T00:00:00ZWeak formulation of elastodynamics in domains with growing cracksTasso, Emanuelehttp://preprints.sissa.it:8180/xmlui/handle/1963/353282019-03-21T01:02:59Z2018-11-01T00:00:00ZWeak formulation of elastodynamics in domains with growing cracks
Tasso, Emanuele
In this paper we formulate and study the system of elastodynamics on domains with arbitrary growing cracks. This includes homogeneous Neumann conditions on the crack sets and mixed general Dirichlet-Neumann conditions on the boundary. The only assumptions on the crack sets are to be (n − 1)-rectifiable with finite surface measure, and increasing in the sense of set inclusions. In particular they might be dense, hence the weak formulation must fall outside the usual context of Sobolev spaces and Korn's inequality.
We prove existence of a solution both for the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance.
2018-11-01T00:00:00Z