Relaxation of Ginzburg–Landau functional perturbed by continuous nonlinear lower-order term in one dimension
2014 ◽
Vol 13
(01)
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pp. 101-123
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We study the asymptotic behavior as ε → 0 of the Ginzburg–Landau functional [Formula: see text], where A(s, v, v′) is the nonlinear lower-order term generated by certain Carathéodory function a : (0, 1)2 × R2 → R. We obtain Γ-convergence for the rescaled functionals [Formula: see text] as ε → 0 by using the notion of Young measures on micropatterns, which was introduced in 2001 by Alberti and Müller. We prove that for ε ≈ 0 the minimal value of [Formula: see text] is close to [Formula: see text], where A∞(s) : = ½A(s, 0, -1) + ½A(s, 0, 1) and where E0 depends only on W. Further, we use this example to establish some general conclusions related to the approach of Alberti and Müller.
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2019 ◽
Vol 53
(2)
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pp. 129-132
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1997 ◽
Vol 46
(3)
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pp. 0-0
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2003 ◽
Vol 82
(1)
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pp. 89
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2012 ◽
Vol 5
(3)
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pp. 507-530
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