A Higher Order Asymptotic Problem Related to Phase Transitions
Roger Moser · SIAM Journal on Mathematical Analysis · 2005
An asymptotic analysis of a family of functionals used in the van der Waals--Cahn--Hilliard theory of phase transitions gives rise to a generalized area functional in the limit. We examine a family of related higher order functionals on a three-dimensional domain. The expected limit in this case is a generalization of the Willmore functional. An analysis of the problem under a monotonicity assumption supports this conjecture.