For variational functionals in Sobolev spaces {W1,p} (1 ≤ p < ∞) we introduce a sequence of so-called dominant "growth estimates" for the gradient of appropriate order of the integrand, each of which guarantees the appropriate level of smoothness of variational functional in the C1-smooth points of the Sobolev space. Earlier studied K-pseudopolynomial representations of the integrand are particular cases of dominant growth estimates.
