SISSA Preprints
http://hdl.handle.net/1963/35281
SISSA authors' not-referred manuscripts of the research outputWed, 31 May 2023 21:58:10 GMT2023-05-31T21:58:10ZValidity and failure of the integral representation of Γ-limits of convex non-local functionals
http://hdl.handle.net/1963/35459
Validity and failure of the integral representation of Γ-limits of convex non-local functionals
Braides, Andrea; Dal Maso, Gianni
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.
Preprint number SISSA/06/2023
Tue, 09 May 2023 00:00:00 GMThttp://hdl.handle.net/1963/354592023-05-09T00:00:00ZΓ-CONVERGENCE AND INTEGRAL REPRESENTATION FOR A CLASS OF FREE DISCONTINUITY FUNCTIONALS
http://hdl.handle.net/1963/35458
Γ-CONVERGENCE AND INTEGRAL REPRESENTATION FOR A CLASS OF FREE DISCONTINUITY FUNCTIONALS
Dal Maso, Gianni; Toader, Rodica
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.
Preprint number:
SISSA 05/2023/MATE
Fri, 05 May 2023 00:00:00 GMThttp://hdl.handle.net/1963/354582023-05-05T00:00:00ZParker Bound and Monopole Pair Production from Primordial Magnetic Fields
http://hdl.handle.net/1963/35457
Parker Bound and Monopole Pair Production from Primordial Magnetic Fields
Kobayashi, Takeshi; Perri, Daniele
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.
SISSA 4/2023/FISI
Tue, 11 Apr 2023 00:00:00 GMThttp://hdl.handle.net/1963/354572023-04-11T00:00:00ZUNIVERSALITY IN THE 2D QUASI-PERIODIC ISING MODEL AND HARRIS-LUCK IRRELEVANCE
http://hdl.handle.net/1963/35456
UNIVERSALITY IN THE 2D QUASI-PERIODIC ISING MODEL AND HARRIS-LUCK IRRELEVANCE
Gallone, Matteo; Mastropietro, Vieri
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.
SISSA 3/2023/MATE
Tue, 04 Apr 2023 00:00:00 GMThttp://hdl.handle.net/1963/354562023-04-04T00:00:00Z