Minimizers for a One-Dimensional Elasticity Problem - Franco, Maria Mercedes
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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.

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Produktbeschreibung
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.
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Autorenporträt
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.