Addendum to ‘Sharp inequalities that generalize the divergence theorem: an extension of the notion of quasi-convexity’

The paper ‘Sharp inequalities that generalize the divergence theorem: an extension of the notion of quasi-convexity’ published inProc. R. Soc. A 2013, 469, 20130075 (doi:10.1098/rspa.2013.0075 ) is clarified. Notably, much more general boundary conditions are given under which sharp lower bounds on the integrals of certain quadratic functions of the fields can be obtained. More precisely, if the quadratic form isQ *-convex then any solution of the Euler–Lagrange equations will necessarily minimize the integral. As a consequence, strictQ *-convexity is found to be an appropriate condition to ensure uniqueness of the solutions of a wide class of linear Euler–Lagrange equations in a given domainΩ with appropriate boundary conditions.