Recently variational problems with nonconvex energies have attracted a lot of attention since they can be used to model materials which display fascinating microstructures. Mathematically speaking, these variational integrals fail to be lower semicontinuous and the classical theory of relaxation states that the associated relaxed problem is again a variational problem with a suitably relaxed energy density. However, these results are only true if suitable growth conditions are satisfied. This talk presents recent results which allow to model incompressible materials or to include the constraint of local preservation of volume. This is joint work with Sergio Conti (Bonn).
Biography
Georg Dolzmann is a professor for mathematics at the University of Regensburg, Germany. After finishing his Ph.D. in Bonn he held postdoctoral appointments in Freiburg and Leipzig and served on the faculty of the Department of Mathematics at the University of Maryland at College Park before accepting his position in Regensburg in 2006. His main research focuses on calculus of variations and nonlinear partial differential equations with an emphasis on nonconvex variational problems and applications to materials science. His further research interests include analytical and numerical methods for problems in elasticity and plasticity.