SISSA Preprints
http://preprints.sissa.it:8080/xmlui/handle/1963/35281
SISSA authors' not-referred manuscripts of the research output2023-01-31T08:07:07ZSome remarks on the convergence of solutions to elliptic equations under weak hypotheses on the data
http://preprints.sissa.it:8080/xmlui/handle/1963/35455
Some remarks on the convergence of solutions to elliptic equations under weak hypotheses on the data
Dal Maso, Gianni; Donati, Davide
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.
Preprin SISSA 20/2022/MATE
2022-12-14T00:00:00ZCompactness for a class of integral functionals with interacting local and non-local terms
http://preprints.sissa.it:8080/xmlui/handle/1963/35454
Compactness for a class of integral functionals with interacting local and non-local terms
Braides, Andrea; Dal Maso, Gianni
We prove a compactness result with respect to -convergence for a class of integral functionals which are expressed as a sum of a local and a non-local term. The main feature is that, under our hypotheses, the local part of the -limit depends on the interaction between the local and non-local terms of the converging subsequence. The result is applied to concentration and homogenization problems.
Preprint SISSA 21/2022/MATE
2022-12-20T00:00:00ZAsymptotic behaviour of the capacity in two-dimensional heterogeneous media
http://preprints.sissa.it:8080/xmlui/handle/1963/35453
Asymptotic behaviour of the capacity in two-dimensional heterogeneous media
Braides, Andrea; Brusca, G.C.
We describe the asymptotic behaviour of the minimal inhomogeneous two-capacity
of small sets in the plane with respect to a fixed open set Ω. This problem is gov erned by two small parameters: ε, the size of the inclusion (which is not restrictive to assume to be a ball), and δ, the period of the inhomogeneity modelled by oscillating coefficients. We show that this capacity behaves as C| log ε| −1. The coefficient C is ex plicitly computed from the minimum of the oscillating coefficient and the determinant of the corresponding homogenized matrix, through a harmonic mean with a proportion depending on the asymptotic behaviour of | log δ|/| log ε|.
Preprint SISSA 10/2022/MATE
2022-06-13T00:00:00ZA note on the homogenization of incommensurate thin films
http://preprints.sissa.it:8080/xmlui/handle/1963/35452
A note on the homogenization of incommensurate thin films
Anello, Irene; Braides, Andrea; Caragiulo, Fabrizio
Dimension-reduction homogenization results for thin films have been obtained under hy potheses of periodicity or almost-periodicity of the energies in the directions of the mid-plane of the film. In this note we consider thin films, obtained as sections of a periodic medium with a mid-plane that may be incommensurate; that is, not containing periods other than oggi si 0. A geometric almost-periodicity argument similar to the cut-and-project argument used for quasicrystals allows to prove a general homogenization result.
Preprint SISSA 22/2022/MATE
2022-12-21T00:00:00Z