A new approach to interior regularity of elliptic systems with quadratic Jacobian structure in dimension two

We prove a new regularity result for systems of nonlinear elliptic equations with quadratic Jacobian type nonlinearity in dimension two. Our proof is based on an adaptation of John Lewis’ method which has not been used for such systems so far. Parts of this work have been done while the second and the third author had been enjoying the hospitality of the Department of Mathematics of the University of Pittsburgh. P.H. was supported by NSF grant DMS-0500966. P.S. was partially supported by the MNiSzW grant no 1 PO 3A 005 29. X.Z. was supported by the Academy of Finland, project 207288.