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We prove regularity theorems for minimizers of integral functionals of the Calculus of Variations∫Ωf(x,Du(x))dx,with non-standard growth conditions of (p,q) type|z|p⩽f(x,z)⩽L(|z|q+1),p<q.In particular, we find that a sufficient condition for minimizers to be regular is qp<n+αn, where the function f(x,z) is α-Hölder continuous with respect to the x-variable and x∈Ω⊂Rn; this condition is also...
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