On conformal variational problems and free boundary continua

On conformal variational problems and free boundary continua

We develop a framework for deriving governing partial differential equations for variational problems on spaces of conformal mappings. The main motivation is to obtain differential equations for the conformal motion of free boundary continua, of interest in image and shape registration. A fundamental tool in the paper, the Hodge–Morrey–Friedrichs decompositions of differential forms on manifold...

Variational Modeling of Parabolic Free Boundary Problems

On Free Boundary Problems

On the Full Regularity of the Free Boundary in a Class of Variational Problems

We consider nonnegative minimizers of the functional

Free Boundary Problems

Paradigmatic examples are the classical Stefan problem and more general models of phase transitions, where the free boundary is the moving interface between phases. Other examples come from problems in surface science, plastic molding and glass rolling, filtration through porous media, where free boundaries occur as fronts between saturated and unsaturated regions, and others from reaction-diff...