A-Variational Principles
Though the A -quasiconvexity condition has been fully explored since its introduction, no explicit examples of associated variational principles have been considered except in the classical curl -case. Our aim is to propose such a family of problems in the div - curl -situation, and explore the corr...
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Published in | Milan journal of mathematics Vol. 91; no. 2; pp. 293 - 314 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
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01.12.2023
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Abstract | Though the
A
-quasiconvexity condition has been fully explored since its introduction, no explicit examples of associated variational principles have been considered except in the classical
curl
-case. Our aim is to propose such a family of problems in the
div
-
curl
-situation, and explore the corresponding
A
-polyconvexity condition as the main structural assumption to ensure weak lower semicontinuity and existence results. |
---|---|
AbstractList | Abstract
Though the
$${\mathcal {A}}$$
A
-quasiconvexity condition has been fully explored since its introduction, no explicit examples of associated variational principles have been considered except in the classical
$${\text {curl}}$$
curl
-case. Our aim is to propose such a family of problems in the
$${\text {div}}{-}{\text {curl}}$$
div
-
curl
-situation, and explore the corresponding
$${\mathcal {A}}$$
A
-polyconvexity condition as the main structural assumption to ensure weak lower semicontinuity and existence results. Though the A -quasiconvexity condition has been fully explored since its introduction, no explicit examples of associated variational principles have been considered except in the classical curl -case. Our aim is to propose such a family of problems in the div - curl -situation, and explore the corresponding A -polyconvexity condition as the main structural assumption to ensure weak lower semicontinuity and existence results. |
Author | Pedregal, Pablo Bandeira, Luís |
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Equ. doi: 10.1007/s005260100092 contributor: fullname: Fonseca – ident: CR5 – volume: 53 start-page: 4178 issue: 4 year: 2021 end-page: 4211 ident: CR20 article-title: -quasiconvexity, Gårding inequalities, and applications in PDE constrained problems in dynamics and statics publication-title: SIAM J. Math. Anal. doi: 10.1137/20M1345128 contributor: fullname: Vikelis – ident: CR28 – ident: CR26 – volume: 234 start-page: 1 issue: 1 year: 2019 end-page: 26 ident: CR4 article-title: Characterizations of symmetric polyconvexity publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-019-01395-4 contributor: fullname: Schlmerkemper – volume: 184 start-page: 1017 issue: 3 year: 2016 ident: 382_CR15 publication-title: Ann. Math. (2) doi: 10.4007/annals.2016.184.3.10 contributor: fullname: P De – volume: 53 start-page: 4178 issue: 4 year: 2021 ident: 382_CR20 publication-title: SIAM J. Math. Anal. doi: 10.1137/20M1345128 contributor: fullname: K Koumatos – volume: 40 start-page: 745 issue: 6 year: 1987 ident: 382_CR19 publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.3160400605 contributor: fullname: RV Kohn – volume: 73 start-page: 279 issue: 4 year: 2016 ident: 382_CR13 publication-title: Port. Math. doi: 10.4171/PM/1988 contributor: fullname: E Davoli – ident: 382_CR25 – volume: 116 start-page: 104 issue: 3 year: 2022 ident: 382_CR27 publication-title: Rev. R. Acad. Cienc. Exactas F’is. Nat. Ser. A Mat. RACSAM doi: 10.1007/s13398-022-01243-3 contributor: fullname: P Pedregal – volume: 61 start-page: 215 issue: 6 year: 2022 ident: 382_CR8 publication-title: Calc. Var. Partial Differ. Equ. doi: 10.1007/s00526-022-02326-0 contributor: fullname: S Conti – start-page: 20 volume-title: Mathematical Elasticity. Vol. I. Three-Dimensional Elasticity. Studies in Mathematics and its Applications year: 1988 ident: 382_CR7 contributor: fullname: PG Ciarlet – volume: 62 start-page: 487 issue: 2 year: 2013 ident: 382_CR1 publication-title: Indiana Univ. Math. J. doi: 10.1512/iumj.2013.62.4928 contributor: fullname: M Baía – volume: 234 start-page: 1 issue: 1 year: 2019 ident: 382_CR4 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-019-01395-4 contributor: fullname: O Boussaid – volume: 245 start-page: 279 issue: 1 year: 2022 ident: 382_CR18 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-022-01775-3 contributor: fullname: A Guerra – volume: 30 start-page: 1355 issue: 6 year: 1999 ident: 382_CR16 publication-title: SIAM J. Math. Anal. doi: 10.1137/S0036141098339885 contributor: fullname: I Fonseca – volume: 63 start-page: 337 year: 1977 ident: 382_CR2 publication-title: Arch. Rational Mech. Anal. doi: 10.1007/BF00279992 contributor: fullname: JM Ball – volume: 53 start-page: 77 issue: 1–2 year: 2018 ident: 382_CR6 publication-title: Meccanica doi: 10.1007/s11012-017-0713-2 contributor: fullname: D Capecchi – ident: 382_CR29 doi: 10.1007/978-3-319-77637-8 – ident: 382_CR30 – volume: 5 start-page: 539 year: 2000 ident: 382_CR3 publication-title: ESAIM Control Optim. Calc. Var. doi: 10.1051/cocv:2000121 contributor: fullname: A Braides – volume: 235 start-page: 841 issue: 2 year: 2020 ident: 382_CR9 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-019-01433-1 contributor: fullname: S Conti – volume: 10 start-page: 49 issue: 1 year: 2017 ident: 382_CR21 publication-title: Adv. Calc. Var. doi: 10.1515/acv-2015-0009 contributor: fullname: J Krämer – volume: 72 start-page: 523 issue: 3 year: 2015 ident: 382_CR23 publication-title: Appl. Math. Optim. doi: 10.1007/s00245-015-9289-1 contributor: fullname: J Matias – ident: 382_CR26 – volume: 55 start-page: Art. 69 issue: 3 year: 2016 ident: 382_CR14 publication-title: Calc. Var. Partial Differ. Equ. doi: 10.1007/s00526-016-0988-5 contributor: fullname: E Davoli – ident: 382_CR28 doi: 10.1007/s00526-019-1544-x – volume-title: Direct Methods in the Calculus of Variations year: 2008 ident: 382_CR11 contributor: fullname: B Dacorogna – ident: 382_CR10 doi: 10.1007/BFb0096144 – volume: 14 start-page: 115 issue: 2 year: 2002 ident: 382_CR12 publication-title: Calc. Var. Partial Differ. Equ. doi: 10.1007/s005260100092 contributor: fullname: B Dacorogna – volume: 2 start-page: 25 year: 1952 ident: 382_CR24 publication-title: Pac. J. Math. doi: 10.2140/pjm.1952.2.25 contributor: fullname: CB Morrey Jr – volume: 60 start-page: 110 issue: 3 year: 2021 ident: 382_CR22 publication-title: Calc. Var. Partial Differ. 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