Research
My area of research is the Calculus of Variations, PDEs, and Geometric Measure Theory with a focus on models in the framework of Continuum Mechanics.
The aim of my doctoral project is to move forward from the current state of art with respect to the characterization of optimal morphologies and elasto-plastic deformation of crystalline materials under critical stress by means of original and new results in the derivation and validation of reliable variational models. The emphasis is both on the static and evolutionary theory with reference in particular to the following two problems:
Existence of solutions of two-phase free-boundary problems,
Dynamical evolution in perfect elasto-plasticity.
Submitted:
J.-F. Babadjian, R. Llerena. Mixed boundary conditions as limits of dissipative boundary conditions in dynamic perfect plasticity, accepted in Journal of Convex Analysis
In preparation:
SDRI model in a two-phase free boundary problem. (In collaboration with P. Piovano)