SISSA OpenScience

SISSA Open Science is a digital repository providing free, open access to SISSA academic scientific production before it is refereed, according to SISSA Regulation on open access (approved in December, 2016).

This repository includes SISSA preprints, unpublished proceedings of conferences held in SISSA, lecture notes and presentations by SISSA professors.

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Recent Submissions

(2023-11-23) Bianchini, Stefano; Leccese, Giacomo Maria
We consider a question posed in [1], namely the blow-up of the PDE ut + (b(t, x)u1+k)x = uxx when b is uniformly bounded, Lipschitz and k = 2. We give a complete answer to the behavior of solutions when b belongs to the Lorentz spaces b ∈ Lp,∞, p ∈ (2,∞], or bx ∈ Lp,∞, p ∈ (1,∞].
Homogenisation problems for free discontinuity functionals with bounded cohesive surface terms
(2023-07-11) Dal Maso, Gianni; Toader, Rodica; mathematics
We study stochastic homogenisation problems for free discontinuity func- tionals under a new assumption on the surface terms, motivated by cohesive fracture models. The results are obtained using a characterization of the limit functional by means of the asymptotic behaviour of suitable minimum problems on cubes with very simple boundary conditions. An important role is played by the subadditive ergodic theorem.
Discrete approximation of nonlocal-gradient energies
(2023-01-22) Braides, Andrea; Causin, Andrea; Solci, Margherita; mathematics
We study a discrete approximation of functionals depending on nonlocal gradients. The discretized functionals are proved to be coercive in classical Sobolev spaces. The key ingredient in the proof is a formulation in terms of circulant Toeplitz matrices.
Another look at elliptic homogenization
(2023-06-21) Braides, Andrea; Cosma Brusca, Giuseppe; Donati, Davide; mathematics
We consider the limit of sequences of normalized (s, 2)-Gagliardo seminorms with an oscillating coefficient as s → 1. In a seminal paper by Bourgain, Brezis and Mironescu (subsequently extended by Ponce) it is proven that if the coefficient is constant then this sequence Γ-converges to a multiple of the Dirichlet integral. Here we prove that, if we denote by ε the scale of the oscillations and we assume that 1−s << ε2, this sequence converges to the homogenized functional formally obtained by separating the effects of s and ε; that is, by the homogenization as ε → 0 of the Dirichlet integral with oscillating coefficient obtained by formally letting s → 1 first.