Second order minimality conditions for functionals with bulk and surface energies
In the first part of the talk we consider the celebrated Mumford-Shah functional and derive a new necessary minimality condition by means of second order nonlocal variations. We then discuss two equivalent formulations of this condition and deduce a local minimality criterion. In the second part of the talk we apply these ideas to a variational model describing the equilibrium configurations of epitaxially strained films.
TUESDAY, December 4, 20007