| Several questions in applied analysis motivated by issues in computer
vision, physics, materials sciences and other areas of engineering may
be treated variationally leading to higher order problems and to models
involving lower dimension density measures. Their study often requires
state-of-the-art techniques, new ideas, and the introduction of
innovative tools in partial differential equations, geometric measure
theory, and the calculus of variations. In this talk it will be shown
how some of these questions may be reduced to well understood first
order problems, while in others the higher order plays a fundamental role.
Applications to phase transitions, to the equilibrium of foams under the
action of surfactants, imaging, micromagnetics and thin films will be
addressed. |
