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 Reviews › RGC 21 - Publication in refereed journal › peer-review
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Detail(s)
Original language | French |
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Pages (from-to) | 563-568 |
Journal / Publication | Comptes Rendus Mathematique |
Volume | 353 |
Issue number | 6 |
Online published | 7 Apr 2015 |
Publication status | Published - Jun 2015 |
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Abstract
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 ǁ∇T∇Φ − ∇ΘT∇ΘǁLq (Ω)
for any q ∈ R such that max{1, p/2 } ≤ q ≤ p, 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 ∇vT + ∇v with respect to the vector field v := Φ - id : Ω → Rn.
Citation Format(s)
Inégalités de Korn non linéaires dans Rn, avec ou sans conditions aux limites. / Ciarlet, Philippe G.; Mardare, Cristinel.
In: Comptes Rendus Mathematique, Vol. 353, No. 6, 06.2015, p. 563-568.
In: Comptes Rendus Mathematique, Vol. 353, No. 6, 06.2015, p. 563-568.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review