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

Abstract

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 \cite{RT21} we heavily exploit careful Fourier space localization methods in distinguishing between the different lamination orders in the data.

34 pages, 6 figures, comments welcome; added argument in Proposition 3.6, corrected typos

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