Singularities and computation of minimizers for variational problems

Various issues axe addressed related to the computation of minimizers for variational problems. Special attention is paid (i) to problems with singular minimizers, which natural numerical schemes may fail to detect, and the role of the choice of function space for such problems, and (ii) to problems for which there is no minimizer, which lead to difficult numerical questions such as the computation of microstructure for elastic materials that undergo phase transformations involving a change of shape.