Published Paper
Inserted: 19 jan 1999
Last Updated: 3 jun 2013
Journal: Calc. Var.
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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