On Artin's Braid Group and Polyconvexity in the Calculus of Variations
نویسنده
چکیده
Let Ω ⊂ 2 be a bounded Lipschitz domain and let F : Ω× 2×2 + −→ be a Carathèodory integrand such that F (x, ·) is polyconvex for L2-a.e. x ∈ Ω. Moreover assume that F is bounded from below and satisfies the condition F (x, ξ) ↘ ∞ as det ξ ↘ 0 for L2-a.e. x ∈ Ω. The paper describes the effect of domain topology on the existence and multiplicity of strong local minimizers of the functional [u] := ∫
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