On conditions for polyconvexity

We give an example of a smooth function f : ℝ2×2 → ℝ, which is not polyconvex and which has the property that its restriction to any ball B ⊂ ℝ2×2 of radius one can be extended to a smooth polyconvex function fB : ℝ2×2 → ℝ. In particular, it implies that there exists no 'local condition' w...