ISOTROPIC AND ANISOTROPIC DOUBLE-PHASE PROBLEMS: OLD AND NEW

We are concerned with the study of two classes of nonlinear problems driven by differential operators with unbalanced growth, which generalize the (p, q)- and (p(x),q(x))-Laplace operators. The associated energy is a double-phase functional, either isotropic or anisotropic. The content of this paper is in relationship with pioneering contributions due to P. Marcellini and G. Mingione.