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A nonlinear Korn inequality on a surface with an explicit estimate of the constant.

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Title: A nonlinear Korn inequality on a surface with an explicit estimate of the constant.
Alternate Title: Une inégalité de Korn non linéaire sur une surface avec une majoration explicite de la constante.
Authors: Malin, Maria1 malinmaria@yahoo.com, Mardare, Cristinel2 cmardare@cityu.edu.hk
Source: Comptes Rendus. Mathématique. 2021, Vol. 359 Issue 1, p105-111. 7p.
Subjects: Vector fields
Abstract (English): A nonlinear Korn inequality on a surface estimates a distance between a surface θ(ω) and another surface φ(ω) in terms of distances between their fundamental forms in the space L p (ω), 1 < p < ∞. We establish a new inequality of this type. The novelty is that the immersion θ belongs to a specific set of mappings of class C ¹ from ω into R ³ with a unit vector field also of class C 1 over ω. [ABSTRACT FROM AUTHOR]
Abstract (French): Une inégalité de Korn non linéaire sur une surface estime une distance entre une surface θ(ω) et une autre surface φ(ω) en fonction des distances entre leur formes fondamentales dans l’espace L p (ω), 1 < p < ∞. Nous établissons une nouvelle inégalité de ce type. La nouveauté réside dans l’appartenance de l’immersion θ à un ensemble particulier d’applications de classe C 1 de ω dans R 3 avec un champ de vecteurs normaux unitaires aussi de classe C 1 dans ω. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:A nonlinear Korn inequality on a surface estimates a distance between a surface θ(ω) and another surface φ(ω) in terms of distances between their fundamental forms in the space L p (ω), 1 < p < ∞. We establish a new inequality of this type. The novelty is that the immersion θ belongs to a specific set of mappings of class C ¹ from ω into R ³ with a unit vector field also of class C 1 over ω. [ABSTRACT FROM AUTHOR]
ISSN:1631073X
DOI:10.5802/crmath.122