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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...

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Bibliographic Details
Main Authors: Raiƫă, Bogdan (Author) , Rüland, Angkana (Author) , Tissot, Camillo (Author)
Format: Article (Journal)
Language:English
Published: 17 March 2023
In: Acta applicandae mathematicae
Year: 2023, Volume: 184, Pages: 1-50
ISSN:1572-9036
DOI:10.1007/s10440-023-00557-7
Online Access:Verlag, kostenfrei, Volltext: https://doi.org/10.1007/s10440-023-00557-7
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Author Notes:Bogdan Raiţă, Angkana Rüland, Camillo Tissot
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Summary: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.
Item Description:Im Titel ist die Zahl 3 tiefgestellt
Gesehen am 24.04.2023
Physical Description:Online Resource
ISSN:1572-9036
DOI:10.1007/s10440-023-00557-7

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