# Rigidity and gamma convergence for solid‐solid phase transitions with SO(2) invariance

@article{Conti2006RigidityAG,
title={Rigidity and gamma convergence for solid‐solid phase transitions with SO(2) invariance},
author={Sergio Conti and Ben Schweizer},
journal={Communications on Pure and Applied Mathematics},
year={2006},
volume={59}
}
• Published 1 June 2006
• Mathematics
• Communications on Pure and Applied Mathematics
The singularly perturbed two‐well problem in the theory of solid‐solid phase transitions takes the form $$I_{\varepsilon}[u] = \int\limits^{}_{\Omega} {1 \over {\varepsilon}} W(\nabla u) + \varepsilon|\nabla^{2}u|^{2},$$ where u : Ω ⊂ ℝn → ℝn is the deformation, and W vanishes for all matrices in K = SO(n)A ∪ SO(n)B. We focus on the case n = 2 and derive, by means of Gamma convergence, a sharp‐interface limit for Iε. The proof is based on a rigidity estimate for low‐energy functions. Our…
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We study the space BD(Ω), composed of vector functions u for which all components εij=1/2(ui, j+uj, i) of the deformation tensor are bounded measures. This seems to be the correct space for the