SISSA Preprints
http://preprints.sissa.it:8180/xmlui/handle/1963/35281
SISSA authors' not-referred manuscripts of the research outputMon, 19 Aug 2019 17:33:38 GMT2019-08-19T17:33:38ZOn the blow-up of GSBV functions under suitable geometric properties of the jump set
http://preprints.sissa.it:8180/xmlui/handle/1963/35337
On the blow-up of GSBV functions under suitable geometric properties of the jump set
Tasso, Emanuele
In this paper we investigate the fine properties of functions under suitable geometric conditions on the jump set. Precisely, given an open set Ω С Rn and given p > 1 we study the blow-up of functions u Є2 GSBV (Ω), whose jump sets belongs to an appropriate class Jp and whose approximate gradient is p-th power summable. In analogy with the theory of p-capacity in the context of Sobolev spaces, we prove that the blow-up of u converges up to a set of Hausdorff dimension less than or equal to n - p. Moreover, we are able to
prove the following result which in the case of W1,p (Ω) functions can be stated as follows: whenever uk strongly converges to u, then up to subsequences, uk pointwise converges to u except on a set whose Hausdorff dimension is at most n - p.
Sat, 01 Jun 2019 00:00:00 GMThttp://preprints.sissa.it:8180/xmlui/handle/1963/353372019-06-01T00:00:00ZOn the approximation of quasistatic evolutions for the debonding of a thin film viavanishing inertia and viscosity
http://preprints.sissa.it:8180/xmlui/handle/1963/35335
On the approximation of quasistatic evolutions for the debonding of a thin film viavanishing inertia and viscosity
Riva, Filippo
In this paper we contribute to studying the issue of quasistatic limit in the context of
Griffith’s theory by investigating a one-dimensional debonding model. It describes the evolution of a thin film partially glued to a rigid substrate and subjected to a vertical loading. Taking friction into account and under suitable assumptions on the toughness of the glue, we prove that, in contrast to what happens in the undamped case, dynamic solutions converge to the quasistatic one when inertia and viscosity go to zero, except for a possible discontinuity at the initial time. We then characterise the size of the jump by means of an asymptotic analysis of the debonding front.
Mon, 24 Jun 2019 00:00:00 GMThttp://preprints.sissa.it:8180/xmlui/handle/1963/353352019-06-24T00:00:00ZA dynamic model for viscoelastic materials with prescribed growing cracks
http://preprints.sissa.it:8180/xmlui/handle/1963/35334
A dynamic model for viscoelastic materials with prescribed growing cracks
Caponi, Maicol; Sapio, Francesco
In this paper we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions we also show a uniqueness result. Finally, we exhibit an example where the energy-dissipation balance is not satisfied, showing there is an additional dissipation due to the crack growth.
Tue, 30 Apr 2019 00:00:00 GMThttp://preprints.sissa.it:8180/xmlui/handle/1963/353342019-04-30T00:00:00ZMassive Higher Spins: Effective Theory and Consistency
http://preprints.sissa.it:8180/xmlui/handle/1963/35333
Massive Higher Spins: Effective Theory and Consistency
Bellazzini, Brando; Riva, Francesco; Serra, Javi; Sgarlata, Francesco
We construct the effective field theory for a single massive higher-spin particle in flat spacetime. Positivity bounds of the S-matrix force the cutoff of the theory
to be well below the naive strong-coupling scale, forbid any potential and make
therefore higher-derivative operators important even at low energy. As interesting
application, we discuss in detail the massive spin-3 theory and show that an extended
Galileon-like symmetry of the longitudinal modes, even with spin, emerges
at high energy.
Sun, 20 Jan 2019 00:00:00 GMThttp://preprints.sissa.it:8180/xmlui/handle/1963/353332019-01-20T00:00:00Z