Univalent solutions of elliptic systems of Heinz-Lewy type

Abstract

Under consideration are homeomorphisms u = (u1(x1, x2), u2(x1, x2)) with finite Dirichlet integral which solve binary, quasilinear elliptic systems (3) with quadratic growth in the gradient of the solution mapping. Regularity results are derived under minimal assumptions on the coefficients of the system. The non-vanishing of the Jacobian is shown for the Heinz-Lewy system (1) together with an a priori estimate from below under suitable normalizations. This involves proving an asymptotic expansion for real-valued functions φ(x) satisfying the differential inequality (2).