Estimates for the constant in two nonlinear Korn inequalities.
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| Title: | Estimates for the constant in two nonlinear Korn inequalities. |
|---|---|
| Authors: | Malin, Maria1 (AUTHOR) cmardare@cityu.edu.hk, Mardare, Cristinel2 (AUTHOR) |
| Source: | Mathematics & Mechanics of Solids. Apr2021, Vol. 26 Issue 4, p471-497. 27p. |
| Subjects: | Tensor fields, k-spaces, Estimates, Differential geometry |
| Abstract: | A nonlinear Korn inequality estimates the distance between two immersions from an open subset of R n into the Euclidean space R k , k ⩾ n ⩾ 1 , in terms of the distance between specific tensor fields that determine the two immersions up to a rigid motion in R k . 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. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics & Mechanics of Solids is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 149494880 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Estimates for the constant in two nonlinear Korn inequalities. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Malin%2C+Maria%22">Malin, Maria</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> cmardare@cityu.edu.hk</i><br /><searchLink fieldCode="AR" term="%22Mardare%2C+Cristinel%22">Mardare, Cristinel</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+%26+Mechanics+of+Solids%22">Mathematics & Mechanics of Solids</searchLink>. Apr2021, Vol. 26 Issue 4, p471-497. 27p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Tensor+fields%22">Tensor fields</searchLink><br /><searchLink fieldCode="DE" term="%22k-spaces%22">k-spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Estimates%22">Estimates</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+geometry%22">Differential geometry</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A nonlinear Korn inequality estimates the distance between two immersions from an open subset of R n into the Euclidean space R k , k ⩾ n ⩾ 1 , in terms of the distance between specific tensor fields that determine the two immersions up to a rigid motion in R k . 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. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics & Mechanics of Solids is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1177/1081286520957705 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 27 StartPage: 471 Subjects: – SubjectFull: Tensor fields Type: general – SubjectFull: k-spaces Type: general – SubjectFull: Estimates Type: general – SubjectFull: Differential geometry Type: general Titles: – TitleFull: Estimates for the constant in two nonlinear Korn inequalities. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Malin, Maria – PersonEntity: Name: NameFull: Mardare, Cristinel IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 10812865 Numbering: – Type: volume Value: 26 – Type: issue Value: 4 Titles: – TitleFull: Mathematics & Mechanics of Solids Type: main |
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