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- W4310264102 abstract "Motivated by complex microstructures in the modelling of shape-memory alloys and by rigidity and flexibility considerations for the associated differential inclusions, in this article we study the energy scaling behaviour of a simplified $m$-well problem without gauge invariances. Considering wells for which the lamination convex hull consists of one-dimensional line segments of increasing order of lamination, we prove that for prescribed Dirichlet data the energy scaling is determined by the emph{order of lamination of the Dirichlet data}. This follows by deducing (essentially) matching upper and lower scaling bounds. For the emph{upper} bound we argue by providing iterated branching constructions, and complement this with ansatz-free emph{lower} bounds. These are deduced by a careful analysis of the Fourier multipliers of the associated energies and iterated bootstrap arguments: based on the ideas from cite{RT21}. Relying on these observations, we study models involving laminates of arbitrary order." @default.
- W4310264102 created "2022-11-30" @default.
- W4310264102 creator A5026729456 @default.
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- W4310264102 date "2021-10-29" @default.
- W4310264102 modified "2023-09-27" @default.
- W4310264102 title "On the Energy Scaling Behaviour of Singular Perturbation Models with Prescribed Dirichlet Data Involving Higher Order Laminates" @default.
- W4310264102 doi "https://doi.org/10.48550/arxiv.2110.15929" @default.
- W4310264102 hasPublicationYear "2021" @default.
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