The Aviles Giga functional

17 November 2003
Dr Andrew Lorent
Take any region omega and let function u defined inside omega be the distance from the boundary, u solves the iconal equation \lt|Du\rt|=1 with boundary condition zero. Functional u is also conjectured (in some cases proved) to be the "limiting minimiser" of various functionals that arise models of blistering and micro magnetics. The precise formulation of these problems involves the notion of gamma convergence. The Aviles Giga functional is a natural "second order" generalisation of the Cahn Hilliard model which was one of the early success of the theory of gamma convergence. These problems turn out to be surprisingly rich with connections to a number of areas of pdes. We will survey some of the more elementary results, describe in detail of one main problems in field and state some partial results.
  • Applied Analysis and Mechanics Seminar