Regularity Theorems for Nonlinear Systems of Partial Differential Equations Under Natural Ellipticity Conditions
Abstract: We consider nonlinear second order elliptic systems in divergence form -D^A^(• , u , D u ) ( • , u , D u ) and prove partial regularity theorems under the ellipticity condition /A(x^,y^,P+D4>)dx > X/|D«>|^dx for all test-vectors  and all points which lies strict between strong ellipticity and the Legendre-condition. We thus obtain an extension of the recent results of Evans for minima of quasiconvex variational integrals as well as a generalisation of the known regularity theorems of Giaquinta, Modica for strongly elliptic systems.