Calculus of Variations and Geometric Measure Theory

E. Davoli - M. Friedrich

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

created by davoli on 15 Oct 2018
modified on 04 Sep 2020


Published Paper

Inserted: 15 oct 2018
Last Updated: 4 sep 2020

Journal: Calc. Var. 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 effective sharp-interface model. The limiting energy is finite only for deformations which have the structure of a laminate. In this case, it is proportional to the total length of the interfaces between the two phases.