Published Paper

Inserted: 19 jan 1999
Last Updated: 5 oct 2025

Journal: Calc. Var. PDE
Volume: 9
Pages: 327-355
Year: 1999

Abstract:

In this paper we study the singular perturbation of $\int (1-
\nabla u
^2)^2$ by $\epsilon^2
\nabla^2u
^2$. 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 $\epsilon^2
\nabla u
^2$, 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.

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