Inserted: 19 jan 1999
Last Updated: 3 jun 2013
Journal: Calc. Var.
In this paper we study the singular perturbation
of $\int (1-
^2)^2$ by $\epsilon^2
^2$. This problem, which could be thought as the natural second order version of the classical singular perturbation of the potential energy $\int (1-u^2)^2$ by $\epsilon^2
^2$, leads, as in the first order case, to energy concentration effects on hypersurfaces. In the two dimensional case we study the natural domain for the limiting energy and prove a compactness theorem in this class.