Some remarks about relaxation problems in the Calculus of Variations
1996 ◽
Vol 126
(3)
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pp. 665-675
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Keyword(s):
We study variational problems for the functional F(u) = ∫Ω f(x, u(x), Lu(x)) dx where u∈uo + V, with Vbeing any closed linear subspace of W2.P(Ω) containing W2.p.0(Ω), Ω is a bounded open set, p > 1, L is a differential operator of second order. We determine the greatest lower semicontinuous function majorised by F for the weak topology of W2.p, for its sequential version if f satisfies no coercivity assumption, showing that in both cases the relaxed functional is expressed in terms of the function ξ↦ f**(x, u, ξ). Finally, an existence result in case f (not necessarily convex) depending only on the Laplacian, is given
2000 ◽
Vol 130
(4)
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pp. 721-741
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1993 ◽
Vol 36
(1)
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pp. 116-122
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1999 ◽
Vol 60
(1)
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pp. 109-118
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1994 ◽
Vol 50
(3)
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pp. 481-499
1991 ◽
Vol 34
(3)
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pp. 412-416
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1999 ◽
Vol 60
(1)
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pp. 163-174
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