Minimizers for a One-Dimensional Elasticity Problem

We study a class of problems in forced phase transitions in one-dimensional, shape-memory solids. The problems incorporate a prescribed body force B which delivers live loading and a non- convex stored energy function of the strain W. The continuity and differentiability requirements over W and B are standard. Assuming that B is concave and under mild growth conditions on W and B, we obtained existence of minimizers for the functional in the problems posed. Then we showed that the minimizers satisfy the Euler-Lagrange equations of equilibrium almost everywhere.

Autorentext

Dr. Maria Mercedes Franco received her Ph.D. in Applied Mathematics from Cornell University in 2005 (USA). She also holds an M.S. in Applied Mathematics from Cornell and a B.S. in Mathematics from Universidad del Valle (Colombia). Her research focuses on problems of nonlinear elasticity, calculus of variations, and numerical analysis.