On the Scaling of the Cubic-to-Tetragonal Phase Transformation with Displacement Boundary Conditions

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2024年7月2日

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Angkana Rüland,
Antonio Tribuzio

摘要

We provide (upper and lower) scaling bounds for a singular perturbation model for the cubic-to-tetragonal phase transformation with (partial) displacement boundary data. We illustrate that the order of lamination of the affine displacement data determines the complexity of the microstructure. As in (Rüland and Tribuzio in ESAIM Control Optim. Calc. Var. 29:68, 2023) we heavily exploit careful Fourier space localization methods in distinguishing between the different lamination orders in the data.