Une inégalité de Korn non linéaire dans ℝn avec une constante majorée explicitement

A nonlinear Korn inequality in ℝn with an explicitly bounded constant

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Original languageFrench
Pages (from-to)621-626
Journal / PublicationComptes Rendus Mathematique
Issue number5
Online published14 Sept 2020
Publication statusPublished - 2020



It is known that the W1,p-distance between an orientation-preserving mapping in W1,p(Ω;ℝn) and another orientation-preserving mapping ΘC1(Ω;ℝn), where Ω is a domain in ℝn, ≥ 2, and > 1 is a real number, is bounded above by the Lp-distance between the square roots of the metric tensor fields induced by these mappings, multiplied by a constant depending only on p, Ω, and Θ
The object of this Note is to establish a better inequality of this type, and to provide in addition an explicitly computable upper bound on the constant appearing in it. An essential role is played in our proofs by the notion of geodesic distance inside an open subset of ℝn.

Research Area(s)

  • Nonlinear Korn inequalities; Nonlinear Elasticity, Shell Theory, Differential Geometry, Surface Theory

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