Lipschitz-continuous local isometric imm
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B. Dacorogna; P. Marcellini; E. Paolini
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Article
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2008
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Elsevier Science
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English
β 702 KB
A rigid map u : Ξ© β R n β R m is a Lipschitz-continuous map with the property that at every x β Ξ© where u is differentiable then its gradient Du(x) is an orthogonal m Γ n matrix. If Ξ© is convex, then u is globally a short map, in the sense that |u(x)u(y)| |x -y| for every x, y β Ξ©; while locally, ar