We discuss variational integrals which are defined on differential forms associated with a given first order elliptic complex. This general framework provides us with better understanding of the concepts of convexity, even in the classical setting $D^{\text{'}}({ℝ}^n,ℝ)\frac{\nabla }{\to }{D}^{\text{'}}({ℝ}^n,{ℝ}^n)\frac{curl}{\to }{D}^{\text{'}}({ℝ}^n,{ℝ}^{n\times n})$