On conditions for polyconvexity

Journal article

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' which is necessary and sufficient for polyconvexity of functions g : ℝn×m → ℝ, where n, m ≥ 2. We also briefly discuss connections with quasiconvexity. © 2000 American Mathematical Society.

Authors: Kristensen, J

• Publication status: Published
• Journal: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
• Volume: 128
• Issue: 6
• Pages: 1793-1797
• Publication date: 2000-01-01
• DOI: 10.1090/S0002-9939-99-05387-3
• ISSN: 0002-9939
• Language: English
• Keywords: rank-1 convexity; quasiconvexity; polyconvexity