Estimates for the constant in two nonlinear Korn inequalities

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)471-497
Journal / PublicationMathematics and Mechanics of Solids
Issue number4
Online published14 Oct 2020
Publication statusPublished - Apr 2021


A nonlinear Korn inequality estimates the distance between two immersions from an open subset of ℝn into the Euclidean space ℝk, kn ≥ 1, in terms of the distance between specific tensor fields that determine the two immersions up to a rigid motion in ℝk. We establish new inequalities of this type in two cases: when k = n, in which case the tensor fields are the square roots of the metric tensor fields induced by the two immersions, and when k = 3 and n = 2, in which case the tensor fields are defined in terms of the fundamental forms induced by the immersions. These inequalities have the property that their constants depend only on the open subset over which the immersions are defined and on three scalar parameters defining the regularity of the immersions, instead of constants depending on one of the immersions, considered as fixed, as up to now.

Research Area(s)

  • differential geometry, nonlinear elasticity, Nonlinear Korn inequalities, shell theory, surface theory