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On weak minima of certain integral functionals. (English) Zbl 0920.49021
The paper deals with the regularity of the weak minima of some integral functionals not necessarily differentiable. By assuming a polynomial growth and a Lipschitz type condition on the integrand, the author proves that a weak minimum \(u\in W^{1,r}_{\text{loc}}\), \(r< p\) (\(p\) is related to the growth of the integrand), is indeed in the space \(W^{1,p}_{\text{loc}}\), if \(r\) is close enough to \(p\). The main arguments in the proof are the Hodge decomposition and some reverse Hölder inequalities.
Reviewer: R.Schianchi (Roma)

49N60 Regularity of solutions in optimal control
49J45 Methods involving semicontinuity and convergence; relaxation
42B25 Maximal functions, Littlewood-Paley theory
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