Moscariello, Gioconda On weak minima of certain integral functionals. (English) Zbl 0920.49021 Ann. Pol. Math. 69, No. 1, 37-48 (1998). 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) Cited in 1 Document MSC: 49N60 Regularity of solutions in optimal control 49J45 Methods involving semicontinuity and convergence; relaxation 42B25 Maximal functions, Littlewood-Paley theory Keywords:regularity; integral functionals; weak minimum; Hodge decomposition; reverse Hölder inequalities PDFBibTeX XMLCite \textit{G. Moscariello}, Ann. Pol. Math. 69, No. 1, 37--48 (1998; Zbl 0920.49021) Full Text: DOI