An identity involving exterior derivatives and applications to Gaffney inequality (Q428409)

The authors prove a generalization of an inequality of Gaffney on a bounded open set of Euclidean space with smooth boundary. They do this by proving a relation between the \(L^2\)-norms of the exterior derivative, codifferential, and covariant derivative of any differential form to some integrals of the normal component and tangential component of that differential form along the boundary.