Maria Mercedes Franco

Minimizers for a One-dimensional Elasticity Problem: Existence and Regularity Results Without Convexity Assumptions Maria Mercedes Franco

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.