Can anyone give me an example of a function $f: \mathbb{R}^{n\times n} \rightarrow \mathbb{R}$, which is separately convex but not rank-one convex? By 'separately convex' I mean convexity in each matrix entry. By 'rank-one convex' I mean convexity in any rank-one direction. I would be totally happy with an example for $n=2$.
Many thanks in advance!