On scaling properties for two-state problems and for a aingularly perturbed T3 structure
In this article we study quantitative rigidity properties for the compatible and incompatible two-state problems for suitable classes of A-free differential inclusions and for a singularly perturbed T3 structure for the divergence operator. In particular, in the compatible setting of the two-state p...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
17 March 2023
|
| In: |
Acta applicandae mathematicae
Year: 2023, Jahrgang: 184, Pages: 1-50 |
| ISSN: | 1572-9036 |
| DOI: | 10.1007/s10440-023-00557-7 |
| Online-Zugang: | Verlag, kostenfrei, Volltext: https://doi.org/10.1007/s10440-023-00557-7
|
| Verfasserangaben: | Bogdan Raiţă, Angkana Rüland, Camillo Tissot |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 1843406799 | ||
| 003 | DE-627 | ||
| 005 | 20240115141753.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 230424s2023 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s10440-023-00557-7 |2 doi | |
| 035 | |a (DE-627)1843406799 | ||
| 035 | |a (DE-599)KXP1843406799 | ||
| 035 | |a (OCoLC)1389530491 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Raiƫă, Bogdan |e VerfasserIn |0 (DE-588)1286814456 |0 (DE-627)1843408503 |4 aut | |
| 245 | 1 | 0 | |a On scaling properties for two-state problems and for a aingularly perturbed T3 structure |c Bogdan Raiţă, Angkana Rüland, Camillo Tissot |
| 246 | 3 | 3 | |a On scaling properties for two-state problems and for a aingularly perturbed T 3 structure |
| 264 | 1 | |c 17 March 2023 | |
| 300 | |a 50 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Im Titel ist die Zahl 3 tiefgestellt | ||
| 500 | |a Gesehen am 24.04.2023 | ||
| 520 | |a In this article we study quantitative rigidity properties for the compatible and incompatible two-state problems for suitable classes of A-free differential inclusions and for a singularly perturbed T3 structure for the divergence operator. In particular, in the compatible setting of the two-state problem we prove that all homogeneous, first order, linear operators with affine boundary data which enforce oscillations yield the typical ϵ23-lower scaling bounds. As observed in Chan and Conti (Math. Models Methods Appl. Sci. 25(06):1091–1124, 2015) for higher order operators this may no longer be the case. Revisiting the example from Chan and Conti (Math. Models Methods Appl. Sci. 25(06):1091–1124, 2015), we show that this is reflected in the structure of the associated symbols and that this can be exploited for a new Fourier based proof of the lower scaling bound. Moreover, building on Rüland and Tribuzio (Arch. Ration. Mech. Anal. 243(1):401–431, 2022); Garroni and Nesi (Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 460(2046):1789–1806, 2004, https://doi.org/10.1098/rspa.2003.1249 [Titel anhand dieser DOI in Citavi-Projekt übernehmen] ); Palombaro and Ponsiglione (Asymptot. Anal. 40(1):37–49, 2004), we discuss the scaling behavior of a T3 structure for the divergence operator. We prove that as in Rüland and Tribuzio (Arch. Ration. Mech. Anal. 243(1):401–431, 2022) this yields a non-algebraic scaling law. | ||
| 650 | 4 | |a 35F05 | |
| 650 | 4 | |a 35Q74 | |
| 650 | 4 | |a 74G99 | |
| 650 | 4 | |a 74N05 | |
| 650 | 4 | |a AA-Free inclusions | |
| 650 | 4 | |a Divergence T3T3 | |
| 650 | 4 | |a Phase transformation | |
| 650 | 4 | |a Two-well problem | |
| 700 | 1 | |a Rüland, Angkana |d 1987- |e VerfasserIn |0 (DE-588)1051987679 |0 (DE-627)787342378 |0 (DE-576)407655506 |4 aut | |
| 700 | 1 | |a Tissot, Camillo |e VerfasserIn |0 (DE-588)1286812224 |0 (DE-627)1843407361 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Acta applicandae mathematicae |d [Erscheinungsort nicht ermittelbar] : Proquest, 1983 |g 184(2023) vom: März, Artikel-ID 5, Seite 1-50 |h Online-Ressource |w (DE-627)271176105 |w (DE-600)1479016-6 |w (DE-576)107585979 |x 1572-9036 |7 nnas |a On scaling properties for two-state problems and for a aingularly perturbed T3 structure |
| 773 | 1 | 8 | |g volume:184 |g year:2023 |g month:03 |g elocationid:5 |g pages:1-50 |g extent:50 |a On scaling properties for two-state problems and for a aingularly perturbed T3 structure |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10440-023-00557-7 |x Verlag |x Resolving-System |z kostenfrei |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20230424 | ||
| 993 | |a Article | ||
| 994 | |a 2023 | ||
| 998 | |g 1286812224 |a Tissot, Camillo |m 1286812224:Tissot, Camillo |d 110000 |d 110200 |d 110000 |d 110400 |e 110000PT1286812224 |e 110200PT1286812224 |e 110000PT1286812224 |e 110400PT1286812224 |k 0/110000/ |k 1/110000/110200/ |k 0/110000/ |k 1/110000/110400/ |p 3 |y j | ||
| 998 | |g 1051987679 |a Rüland, Angkana |m 1051987679:Rüland, Angkana |p 2 | ||
| 999 | |a KXP-PPN1843406799 |e 4312909784 | ||
| BIB | |a Y | ||
| SER | |a journal | ||
| JSO | |a {"title":[{"title":"On scaling properties for two-state problems and for a aingularly perturbed T3 structure","title_sort":"On scaling properties for two-state problems and for a aingularly perturbed T3 structure"}],"person":[{"role":"aut","roleDisplay":"VerfasserIn","display":"Raiƫă, Bogdan","given":"Bogdan","family":"Raiƫă"},{"roleDisplay":"VerfasserIn","display":"Rüland, Angkana","role":"aut","family":"Rüland","given":"Angkana"},{"role":"aut","display":"Tissot, Camillo","roleDisplay":"VerfasserIn","given":"Camillo","family":"Tissot"}],"titleAlt":[{"title":"On scaling properties for two-state problems and for a aingularly perturbed T 3 structure"}],"recId":"1843406799","language":["eng"],"note":["Im Titel ist die Zahl 3 tiefgestellt","Gesehen am 24.04.2023"],"type":{"bibl":"article-journal","media":"Online-Ressource"},"id":{"eki":["1843406799"],"doi":["10.1007/s10440-023-00557-7"]},"origin":[{"dateIssuedKey":"2023","dateIssuedDisp":"17 March 2023"}],"name":{"displayForm":["Bogdan Raiţă, Angkana Rüland, Camillo Tissot"]},"relHost":[{"title":[{"title":"Acta applicandae mathematicae","subtitle":"an international survey journal on applying mathematics and mathematical applications","title_sort":"Acta applicandae mathematicae"}],"pubHistory":["1.1983 -"],"part":{"pages":"1-50","year":"2023","extent":"50","text":"184(2023) vom: März, Artikel-ID 5, Seite 1-50","volume":"184"},"note":["Gesehen am 06.12.05"],"type":{"media":"Online-Ressource","bibl":"periodical"},"disp":"On scaling properties for two-state problems and for a aingularly perturbed T3 structureActa applicandae mathematicae","recId":"271176105","language":["eng"],"origin":[{"dateIssuedDisp":"1983-","publisher":"Proquest ; Springer Science + Business Media B.V ; Kluwer","dateIssuedKey":"1983","publisherPlace":"[Erscheinungsort nicht ermittelbar] ; Dordrecht [u.a.] ; Dordrecht [u.a.]"}],"id":{"zdb":["1479016-6"],"eki":["271176105"],"issn":["1572-9036"]},"physDesc":[{"extent":"Online-Ressource"}]}],"physDesc":[{"extent":"50 S."}]} | ||
| SRT | |a RAIABOGDANONSCALINGP1720 | ||