Inégalités de Korn non linéaires dans Rn, avec ou sans conditions aux limites

Nonlinear Korn inequalities in Rn, with or without boundary conditions

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Original languageFrench
Pages (from-to)563-568
Journal / PublicationComptes Rendus Mathematique
Issue number6
Online published7 Apr 2015
Publication statusPublished - Jun 2015


Let Ω be a bounded open subset of Rn with a Lipschitz boundary. Given two smooth enough immersions Φ : Ω → Rn et Θ : Ω → Rn with the same orientation, we establish various nonlinear Korn inequalities that show that, for any 1 < p < ∞, the norm ǁΦ − ΘǁW1,p (Ω) can be bounded above in terms of the norm ǁT∇Φ∇ΘT∇ΘǁLq (Ω) for any q ∈ R such that max{1, p/2 } ≤ qp, where (∇ΘT∇Φ - ∇ΘT∇Θ) thus represents the exact difference between the metrics corresponding to the immersions Φ and Θ. Such inequalities generalize the well-known linear Korn inequalities, where, when Θ = id, the exact difference ∇ΦT∇Φ - I is reduced to its linear part vv with respect to the vector field v :Φ id : Ω → Rn.