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 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.12.2023
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| Subjects | |
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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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| References | Conti, Gmeineder (CR8) 2022; 61 Krämer, Krömer, Kružík, Pathó (CR21) 2017; 10 Fonseca, Müller (CR16) 1999; 30 Braides, Fonseca, Leoni (CR3) 2000; 5 Baía, Matias, Santos (CR1) 2013; 62 Maestre, Pedregal (CR22) 2021; 60 Davoli, Fonseca (CR14) 2016; 55 Dacorogna (CR11) 2008 CR10 CR31 Fonseca, Leoni, Müller (CR17) 2004; 21 CR30 Dacorogna, Fonseca (CR12) 2002; 14 Koumatos, Vikelis (CR20) 2021; 53 Pedregal (CR27) 2022; 116 Davoli, Fonseca (CR13) 2016; 73 Guerra, Raiţă (CR18) 2022; 245 CR5 Morrey (CR24) 1952; 2 Conti, Müller, Ortiz (CR9) 2020; 235 CR29 Kohn, Vogelius (CR19) 1987; 40 CR28 Ciarlet (CR7) 1988 CR26 CR25 Boussaid, Kreisbeck, Schlmerkemper (CR4) 2019; 234 De, Guido (CR15) 2016; 184 Matias, Morandotti, Santos (CR23) 2015; 72 Ball (CR2) 1977; 63 Capecchi, Favata, Ruta (CR6) 2018; 53 I Fonseca (382_CR16) 1999; 30 RV Kohn (382_CR19) 1987; 40 382_CR10 O Boussaid (382_CR4) 2019; 234 PG Ciarlet (382_CR7) 1988 M Baía (382_CR1) 2013; 62 P Pedregal (382_CR27) 2022; 116 382_CR5 E Davoli (382_CR13) 2016; 73 F Maestre (382_CR22) 2021; 60 B Dacorogna (382_CR12) 2002; 14 J Matias (382_CR23) 2015; 72 CB Morrey Jr (382_CR24) 1952; 2 A Guerra (382_CR18) 2022; 245 JM Ball (382_CR2) 1977; 63 382_CR26 K Koumatos (382_CR20) 2021; 53 382_CR25 382_CR28 A Braides (382_CR3) 2000; 5 E Davoli (382_CR14) 2016; 55 B Dacorogna (382_CR11) 2008 382_CR29 I Fonseca (382_CR17) 2004; 21 J Krämer (382_CR21) 2017; 10 S Conti (382_CR8) 2022; 61 P De (382_CR15) 2016; 184 D Capecchi (382_CR6) 2018; 53 382_CR31 382_CR30 S Conti (382_CR9) 2020; 235 |
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Anal. doi: 10.1007/s00205-019-01433-1 contributor: fullname: Ortiz – volume: 184 start-page: 1017 issue: 3 year: 2016 end-page: 1039 ident: CR15 article-title: Filip on the structure of -free measures and applications publication-title: Ann. Math. (2) doi: 10.4007/annals.2016.184.3.10 contributor: fullname: Guido – volume: 30 start-page: 1355 issue: 6 year: 1999 end-page: 1390 ident: CR16 article-title: -quasiconvexity, lower semicontinuity, and Young measures publication-title: SIAM J. Math. Anal. doi: 10.1137/S0036141098339885 contributor: fullname: Müller – volume: 5 start-page: 539 year: 2000 end-page: 577 ident: CR3 article-title: -quasiconvexity: relaxation and homogenization publication-title: ESAIM Control Optim. Calc. Var. doi: 10.1051/cocv:2000121 contributor: fullname: Leoni – ident: CR30 – ident: CR10 – volume: 63 start-page: 337 year: 1977 end-page: 403 ident: CR2 article-title: Convexity conditions and existence theorems in nonlinear elasticity publication-title: Arch. 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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. Equ. doi: 10.1007/s00526-021-01945-3 contributor: fullname: F Maestre – ident: 382_CR5 – ident: 382_CR31 doi: 10.1007/978-1-4613-8360-4_12 – volume: 21 start-page: 209 issue: 2 year: 2004 ident: 382_CR17 publication-title: Ann. Inst. H. Poincaré C Anal. Non Linéaire doi: 10.1016/j.anihpc.2003.01.003 contributor: fullname: I Fonseca |
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