Regularity Results for the Generalized Beltrami System

For the generalized Beltrami system with two characteristic matrices, we deal with the regularity of its very weak solutions in the Sobolev class W1,rloc(,Rn) (1 > r > n). By changing the generalized Beltrami system into a class of a divergent elliptic system with nonhomogeneous items, we obtain that each of its very weak solutions is essentially a classical weak solution of a usual Sobolev class. Furthermore, we also establish a higher regularity of its weak solution if the regularity hypotheses of two characteristic matrices are improved.