Remarks on morrey’s quasi-convexity

We revisit the question of whether the functions defined of the real m × n matrices that are convex along rank-one directions are also quasi-convex in the sense of Morrey. Using the linearity of the map f → ∫_Tn f(∇u(x)) dx, we propose to study the question as a problem in convex optimization. This might be useful when trying to resolve the open cases, such as the case m = 2, or various cases with symmetries.