Calculus of Variations and Geometric Measure Theory

A. Ruland - A. Tribuzio

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

created by tribuzio on 18 Jul 2023
modified on 02 Jul 2024


Published Paper

Inserted: 18 jul 2023
Last Updated: 2 jul 2024

Journal: J. Elast.
Year: 2024
Doi: 10.1007/s10659-024-10075-8

ArXiv: 2306.05740 PDF


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.