Integrability For Minimizers Of Some Functionals And Solutions To Elliptic Systems

In this paper a local regularity result is obtained for minimizers of integral functionals of the typewhere the Caratheodory function f(x,u,Du)= fo(x,u,Du)+ f1(x,u,Du),fo(x,s,z)satis-fies some growth conditions and f1(x,s,z)satisfies some conditions.We also consider local regularity and local boundedness for solutions of nonhomogeneous elliptic problems whose type isMoreover,we consider the max-min principle for vector valued minimizers of some functionals and the maximum and minimum principle for weak solutions u of some elliptic systems.At last we consider higher integrability for very weak solutions of A-harmonic equation.