Harnack inequalities for quasi-minima of variational integrals

In his fundamental work on linear elliptic equations, De Giorgi established local bounds and Holder estimates for functions satisfying certain integral inequalities. The main result of this paper is that the Harnack inequality can be proved directly for functions in the De Giorgi classes. This implies that every non-negative Q-minimum (in the terminology of Giaquinta and Giusti) satisfies a Harnack inequality.