Regularity Results for the Generalized Beltrami System

For the generalized Beltrami system with two characteristic matrices,we deal with theregularity of its very weak solutions in the Sobolev class W(Ω,R~n)(1<r<n).By changing thegeneralized Beltraini system into a class of a divergent elliptic system with nonhomogeneous items,weobtain that each of its very weak solutions is essentially a classical weak solution of a usual Sobolevclass.Furthermore,we also establish a higher regularity of its weak solution if the regularity hypothesesof two characteristic matrices are improved.