(Mathematical Institute, Oxford University)
ENERGY MINIMIZATION AND SINGULARITIES:
a guided tour of the calculus of variations and its
applications to nonlinear materials.
The second law of thermodynamics motivates the search for energy-minimizing
configurations of materials and the study of their stability. The calculus
of variations should tell us whether such configurations exist and what they
look like. For nonlinear materials such as alloys or liquid crystals the
corresponding energy functionals may or may not have minimizers, while if
they exist minimizers can be singular. The lecture will describe some of
the interesting conceptual, analytic and computational issues that arise
in this area.