  We are concerned with a variant of the isoperimetric problem, which in our
setting arises in a geometrically nonlinear two-well problem in elasticity.
More precisely, we investigate the optimal scaling of the energy of an elastic
inclusion of a fixed volume for which the energy is determined by a surface and
an (anisotropic) elastic contribution. Following ideas from \cite{CS} and
\cite{KnuepferKohn-2011}, we derive the lower scaling bound by invoking a
two-well rigidity argument and a covering result. The upper bound follows from
a well-known construction for a lens-shaped elastic inclusion.
