Growth conditions and regularity for weak solutions to nonlinear elliptic pdes

We describe some aspects of the process/approach to interior regularity of weak solutionsto a class of nonlinear elliptic equations in divergence form, as well as of minimizersof integrals of the calculus of variations. In particular with respect to the growth conditionswe emphasize some differences between solving equations and minimizing energy integrals, and also between x−dependence or x−independence.