Two-well rigidity and multidimensional sharp-interface limits for solid–solid phase transitions

@article{Davoli2020TwowellRA,
  title={Two-well rigidity and multidimensional sharp-interface limits for solid–solid phase transitions},
  author={Elisa Davoli and Manuel Friedrich},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2020}
}
We establish a quantitative rigidity estimate for two-well frame-indifferent nonlinear energies, in the case in which the two wells have exactly one rank-one connection. Building upon this novel rigidity result, we then analyze solid-solid phase transitions in arbitrary space dimensions, under a suitable anisotropic penalization of second variations. By means of $\Gamma$-convergence, we show that, as the size of transition layers tends to zero, singularly perturbed two-well problems approach an… 
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