Regularity for some scaler variational problems under general growth conditions

We consider integrals of the calculus of variations over a set Omega of R '' and the related regularity result: are the minimizers smooth0 functions, say for example of class C-infinity(Omega)? Classically, the so-called natural growth conditions on the integrand have been the main sufficient assumptions for regularity. In recent years, motivated also by application, the interest in the study of this problem has increased under more general growth assumptions. In this paper, we propose some general growth conditions that guarantee regularity for a class of scalar variational problems.