What does rank-one convexity have to do with viscosity solutions?
In this paper, based on Hilbert's theorem for positive polynomials, it is proved that rank-one convex functions associated with \(2 \times 2\)-matrices admit a decomposition as a sum of a multiple of the corresponding determinant and a viscosity solution for a certain equation. For the entire collection see [Zbl 1395.00083].
Hilbert's theorem for positive polynomials
scientific article; zbMATH DE number 7009756