Tuesday, 18 December 2018, 3 p.m. (sharp),
Dr. Elisa Davoli, Università di Vienna
at the conference room of IMATI-CNR in Pavia, will give a lecture titled:
Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions
as part of the Applied Mathematics Seminar (IMATI-CNR e Dipartimento di Matematica, Pavia).
At the end a refreshment will be organized.
Abstract. In this talk 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 any 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 tend 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 size of the interfaces between the two phases.