Lipschitz Bounds and Nonautonomous Integrals

Abstract We provide a general approach to Lipschitz regularity of solutions for large class vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range from those with unbalanced polynomial growth conditions fast, exponential type growth. results obtained are sharp respect all the data and also yield new, optimal criteria in classical uniformly elliptic case. give classification different types ellipticity, accordingly identifying suitable get theorems.