GENERALIZED MULTISCALE YOUNG MEASURES.
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| Title: | GENERALIZED MULTISCALE YOUNG MEASURES. |
|---|---|
| Authors: | ARROYO-RABASA, ADOLFO1 adolforabasa@gmail.com, DIERMEIER, JOHANNES2 diermeier@posteo.de |
| Source: | SIAM Journal on Mathematical Analysis. 2020, Vol. 52 Issue 4, p3252-3300. 49p. |
| Subjects: | Oscillations, Mathematics, Integrals |
| Abstract: | This paper is devoted to the construction of generalized multiscale Young measures, which are the extension of Pedregal's multiscale Young measures [Trans. Amer. Math. Soc., 358 (2006), pp. 591-602] to the setting of generalized Young measures introduced by DiPerna and Majda [Comm. Math. Phys., 108 (1987), pp. 667-689]. As a tool for variational problems, these are well-suited objects for the study (at different length-scales) of oscillation and concentration effects of convergent sequences of measures. Important properties of multiscale Young measures such as compactness, representation of nonlinear compositions, localization principles, and differential constraints are extensively developed in the second part of this paper. As an application, we use this framework to address the Γ-limit characterization of the homogenized limit of convex integrals defined on spaces of measures satisfying a general linear PDE-constraint. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Mathematical Analysis is the property of Society for Industrial & Applied Mathematics 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: 147866430 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: GENERALIZED MULTISCALE YOUNG MEASURES. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22ARROYO-RABASA%2C+ADOLFO%22">ARROYO-RABASA, ADOLFO</searchLink><relatesTo>1</relatesTo><i> adolforabasa@gmail.com</i><br /><searchLink fieldCode="AR" term="%22DIERMEIER%2C+JOHANNES%22">DIERMEIER, JOHANNES</searchLink><relatesTo>2</relatesTo><i> diermeier@posteo.de</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Mathematical+Analysis%22">SIAM Journal on Mathematical Analysis</searchLink>. 2020, Vol. 52 Issue 4, p3252-3300. 49p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Oscillations%22">Oscillations</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Integrals%22">Integrals</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper is devoted to the construction of generalized multiscale Young measures, which are the extension of Pedregal's multiscale Young measures [Trans. Amer. Math. Soc., 358 (2006), pp. 591-602] to the setting of generalized Young measures introduced by DiPerna and Majda [Comm. Math. Phys., 108 (1987), pp. 667-689]. As a tool for variational problems, these are well-suited objects for the study (at different length-scales) of oscillation and concentration effects of convergent sequences of measures. Important properties of multiscale Young measures such as compactness, representation of nonlinear compositions, localization principles, and differential constraints are extensively developed in the second part of this paper. As an application, we use this framework to address the Γ-limit characterization of the homogenized limit of convex integrals defined on spaces of measures satisfying a general linear PDE-constraint. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Mathematical Analysis is the property of Society for Industrial & Applied Mathematics 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: 10.1137/19M1238848 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 49 StartPage: 3252 Subjects: – SubjectFull: Oscillations Type: general – SubjectFull: Mathematics Type: general – SubjectFull: Integrals Type: general Titles: – TitleFull: GENERALIZED MULTISCALE YOUNG MEASURES. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: ARROYO-RABASA, ADOLFO – PersonEntity: Name: NameFull: DIERMEIER, JOHANNES IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: 2020 Type: published Y: 2020 Identifiers: – Type: issn-print Value: 00361410 Numbering: – Type: volume Value: 52 – Type: issue Value: 4 Titles: – TitleFull: SIAM Journal on Mathematical Analysis Type: main |
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