Uniqueness of Equilibrium Configurations in Solid Crystals
نویسندگان
چکیده
In this article, under suitable assumptions, it is proved that infu∈UΛ E[u] is dual to sup(a,b){ ∫ Ω a(F(x))dx + ∫ Λ b(y)dy}, where, E[u] := ∫ Ω(h(detDu) − F · u)dx. Here, the infimum is performed over UΛ, the set of all orientation-preserving deformations u ∈ C1(Ω)d that are homeomorphisms from Ω̄ onto Λ̄, and the supremum is performed over the set of all upper semicontinuous functions a, b such that a(z) +αb(y) ≤ h(α)− y · z. This duality result turns out to be important in the study of existence and uniqueness of smooth minimizers of E. Note that M → h(detM) is not coercive and thus direct methods of the calculus of variations don’t apply here.
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عنوان ژورنال:
- SIAM J. Math. Analysis
دوره 32 شماره
صفحات -
تاریخ انتشار 2000