Singular Limits of Variational Problems
This area of research explores a class of geometric variational problems
that have their origin in a variety of physical phenomena. These include
pattern formation in optical, fluid and biological systems which are
driven far from threshold as well as defect formation in elastic materials
and micromagnetic films. Mathematically, these variational problems are based
on a functional of the form of a Ginzburg-Landau energy but in which the
variations are taken over gradient vector or even director fields rather than
arbitrary vector fields. What is of particular interest is to describe the
defects which arise in the limit as a regularizing term in the energy is taken
to zero.
