# 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} }

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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