HOMOGENIZATION OF ENERGIES DEFINED ON PAIRS SET-FUNCTION
2009 ◽
Vol 11
(03)
◽
pp. 459-479
◽
Keyword(s):
Open Set
◽
In the present work, we deal with the problem of the asymptotic behavior of a sequence of non-homogeneous energies depending on a pair set-function of the form [Formula: see text] with u ∈ H1(Ω), E regular open set and the energy densities f and φ both 1-periodic in the first variable; this leads, in the Γ-limit, to a problem of homogenization. We prove a Γ-convergence result for the sequence {Fε}, showing that there is no interaction between the homogenized bulk and surface energy density; that is, even though the effect of the bulk and surface energies are at the same energy scale, oscillations in the bulk term can be neglected close to the surfaces ∂*E and S(u), where surface oscillations are dominant.
2006 ◽
Vol 27
(6)
◽
pp. 615-636
1997 ◽
Vol 8
(3)
◽
pp. 293-299
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Keyword(s):
2020 ◽
Vol 60
(8-9)
◽
pp. 805-822
◽
2019 ◽
Vol 484
◽
pp. 184-188
◽
Keyword(s):
1994 ◽
Vol 04
(03)
◽
pp. 373-407
◽
1996 ◽
Vol 06
(02)
◽
pp. 227-244
◽
Keyword(s):