PreprintsPreprint papershttps://openscience.sissa.it/handle/1963/352822024-03-05T04:45:48Z2024-03-05T04:45:48Z4841A closure theorem for gAMMA-convergence and H-convergence with applications to non-periodic homogenizationBraides, AndreaDal Maso, GianniLe Bris, Claudehttps://openscience.sissa.it/handle/1963/354712024-03-05T00:20:54Z2024-02-29T00:00:00Zdc.title: A closure theorem for gAMMA-convergence and H-convergence with applications to non-periodic homogenization
dc.contributor.author: Braides, Andrea; Dal Maso, Gianni; Le Bris, Claude
dc.description.abstract: In this work we examine the stability of some classes of integrals, and in particular
with respect to homogenization. The prototypical case is the homogenization of
quadratic energies with periodic coe cients perturbed by a term vanishing at in nity,
which has been recently examined in the framework of elliptic PDE.We use localization
techniques and higher-integrability Meyers-type results to provide a closure theorem by
gamma-convergence within a large class of integral functionals. From such result we derive
stability theorems in homogenization which comprise the case of perturbations with
zero average on the whole space. The results are also extended to the stochastic case,
and specialized to the G-convergence of operators corresponding to quadratic forms. A
corresponding analysis is also carried on for non-symmetric operators using the localization
properties of H-convergence. Finally, we treat the case of perforated domains
with Neumann boundary condition, and their stability.
dc.description: SISSA 3/2024/MATE
2024-02-29T00:00:00ZEXISTENCE AND BLOW-UP FOR NON-AUTONOMOUS SCALAR CONSERVATION LAWS WITH VISCOSITYBianchini, StefanoLeccese, Giacomo Mariahttps://openscience.sissa.it/handle/1963/354702024-02-16T00:20:35Z2023-11-23T00:00:00Zdc.title: EXISTENCE AND BLOW-UP FOR NON-AUTONOMOUS SCALAR CONSERVATION LAWS WITH VISCOSITY
dc.contributor.author: Bianchini, Stefano; Leccese, Giacomo Maria
dc.description.abstract: 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,∞].
dc.description: SISSA 15/2023/MATE
2023-11-23T00:00:00ZHomogenisation problems for free discontinuity functionals with bounded cohesive surface termsDal Maso, GianniToader, Rodicahttps://openscience.sissa.it/handle/1963/354622023-07-11T23:20:44Z2023-07-11T00:00:00Zdc.title: Homogenisation problems for free discontinuity functionals with bounded cohesive surface terms
dc.contributor.author: Dal Maso, Gianni; Toader, Rodica
dc.description.abstract: 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.
2023-07-11T00:00:00ZDiscrete approximation of nonlocal-gradient energiesBraides, AndreaCausin, AndreaSolci, Margheritahttps://openscience.sissa.it/handle/1963/354612023-06-22T23:20:46Z2023-01-22T00:00:00Zdc.title: Discrete approximation of nonlocal-gradient energies
dc.contributor.author: Braides, Andrea; Causin, Andrea; Solci, Margherita
dc.description.abstract: 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.
dc.description: SISSA 09/2023/MATE
2023-01-22T00:00:00ZAnother look at elliptic homogenizationBraides, AndreaCosma Brusca, GiuseppeDonati, Davidehttps://openscience.sissa.it/handle/1963/354602023-06-21T23:20:43Z2023-06-21T00:00:00Zdc.title: Another look at elliptic homogenization
dc.contributor.author: Braides, Andrea; Cosma Brusca, Giuseppe; Donati, Davide
dc.description.abstract: 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.
2023-06-21T00:00:00ZValidity and failure of the integral representation of Γ-limits of convex non-local functionalsBraides, AndreaDal Maso, Giannihttps://openscience.sissa.it/handle/1963/354592023-05-10T23:20:43Z2023-05-09T00:00:00Zdc.title: Validity and failure of the integral representation of Γ-limits of convex non-local functionals
dc.contributor.author: Braides, Andrea; Dal Maso, Gianni
dc.description.abstract: We prove an integral-representation result for limits of non-local quadratic forms on H1
0 pΩq, with Ω a bounded open subset of Rd, extending the representation on C8c
pΩq given by the Beurling-Deny formula in the theory of Dirichlet forms. We give
a counterexample showing that a corresponding representation may not hold if we
consider analogous functionals in W1,p0 pΩq, with p ‰ 2 and 1 ă p ď d.
dc.description: Preprint number SISSA/06/2023
2023-05-09T00:00:00ZΓ-CONVERGENCE AND INTEGRAL REPRESENTATION FOR A CLASS OF FREE DISCONTINUITY FUNCTIONALSDal Maso, GianniToader, Rodicahttps://openscience.sissa.it/handle/1963/354582023-05-19T06:51:41Z2023-05-05T00:00:00Zdc.title: Γ-CONVERGENCE AND INTEGRAL REPRESENTATION FOR A CLASS OF FREE DISCONTINUITY FUNCTIONALS
dc.contributor.author: Dal Maso, Gianni; Toader, Rodica
dc.description.abstract: We study the Γ -limits of sequences of free discontinuity functionals with
linear growth, assuming that the surface energy density is bounded. We determine the
relevant properties of the Γ -limit, which lead to an integral representation result by
means of integrands obtained by solving some auxiliary minimum problems on small
cubes.
dc.description: Preprint number:
SISSA 05/2023/MATE
2023-05-05T00:00:00ZParker Bound and Monopole Pair Production from Primordial Magnetic FieldsKobayashi, TakeshiPerri, Danielehttps://openscience.sissa.it/handle/1963/354572023-04-11T23:20:47Z2023-04-11T00:00:00Zdc.title: Parker Bound and Monopole Pair Production from Primordial Magnetic Fields
dc.contributor.author: Kobayashi, Takeshi; Perri, Daniele
dc.description.abstract: We present new bounds on the cosmic abundance of magnetic monopoles based
on the survival of primordial magnetic fields during the reheating and radiation-dominated
epochs. The new bounds can be stronger than the conventional Parker bound from galactic magnetic fields, as well as bounds from direct searches. We also apply our bounds to monopoles produced by the primordial magnetic fields themselves through the Schwinger effect, and derive additional conditions for the survival of the primordial fields.
dc.description: SISSA 4/2023/FISI
2023-04-11T00:00:00ZUNIVERSALITY IN THE 2D QUASI-PERIODIC ISING MODEL AND HARRIS-LUCK IRRELEVANCEGallone, MatteoMastropietro, Vierihttps://openscience.sissa.it/handle/1963/354562023-04-11T23:20:45Z2023-04-04T00:00:00Zdc.title: UNIVERSALITY IN THE 2D QUASI-PERIODIC ISING MODEL AND HARRIS-LUCK IRRELEVANCE
dc.contributor.author: Gallone, Matteo; Mastropietro, Vieri
dc.description.abstract: We prove that in the 2d Ising Model with a weak bidimensional quasi-periodic
disorder in the interaction, the critical behavior is the same as in the non-disordered case, that is the critical exponents are identical and no logarithmic corrections are present. The result establishes the validity of the prediction based on the Harris-Luck criterion and it provides the first rigorous proof of universality in the Ising model in presence of quasi-periodic disorder. The proof combines Renormalization Group approaches with direct methods used to deal with small divisors in KAM theory.
dc.description: SISSA 3/2023/MATE
2023-04-04T00:00:00ZGamma-convergence of quadratic functionals perturbed by bounded linear functionalsDal Maso, GianniDonati, Davidehttps://openscience.sissa.it/handle/1963/354552023-09-27T23:20:44Z2022-12-14T00:00:00Zdc.title: Gamma-convergence of quadratic functionals perturbed by bounded linear functionals
dc.contributor.author: Dal Maso, Gianni; Donati, Davide
dc.description.abstract: We study the asymptotic behavior of solutions to elliptic equations of the
form (div(Akruk) = fk in ;uk = wk on @;
where Rn is a bounded open set, wk is weakly converging in H1(), fk is weakly
converging in H1(), and Ak is a sequence square matrices satisfying some uniform
ellipticity and boundedness conditions, and H-converging in . In particular, we characterize
the weak limits of the solutions uk and of their momenta Akruk . When Ak is symmetric and wk = w = 0, we characterize the limits of the energies for the solutions.
dc.description: Preprin SISSA 20/2022/MATE
2022-12-14T00:00:00Z