DSpace 7

DSpace is the world leading open source repository platform that enables organisations to:

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Communities in DSpace

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Now showing 1 - 4 of 4

Recent Submissions

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Marie Slodowska Curie Actions Postdoctoral Fellowship (PF)
(2023-08-31) de Luca, Mariarita
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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.
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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.
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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.
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Validity and failure of the integral representation of Γ-limits of convex non-local functionals
(2023-05-09) Braides, Andrea; Dal Maso, Gianni; mathematics
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.