Isoperimetric inequality for Div-curl fields

Let (E, B) be a Holder conjugate pair of vector fields, both belonging to the space L(2n-2)/n(R-n; R-n). Suppose that div B = 0 and curl E = 0. In this paper we prove the following isoperimetric type inequality [GRAPHICS] where J(x, F) = [E, B] and \F\(2) = \E\(2) + \B\(2). As an application, we recover Holder continuity for solutions of n-Laplace equation div(\delu\(n-2)delu) = 0.