Esposito, L.; Mingione, G. A regularity theorem for \(\omega\)-minimizers of integral functionals. (English) Zbl 0949.49023 Rend. Mat. Appl., VII. Ser. 19, No. 1, 17-44 (1999). From the authors’ abstract: “We prove local Hölder continuity of the \(\omega\)-minimizers of the integral functional \(\int_\Omega f(x,u,Du)\), where the Carathéodory function \(f\) satisfies the following growth condition \[ |Du|^p- b(x)|u|^\gamma- a(x)\leq f(x,u,Du)\leq L(|Du|^p+ b(x)|u|^\gamma+ a(x)), \] where \(L\geq 1\), \(1<p\leq \gamma< p^*\) and \(a(x)\), \(b(x)\) are two nonnegative functions that lie in suitable \(L^p\) spaces”. Reviewer: M.Fuchs (Saarbrücken) Cited in 5 Documents MSC: 49N60 Regularity of solutions in optimal control 49N45 Inverse problems in optimal control 35J20 Variational methods for second-order elliptic equations Keywords:minimizers of integral functionals; regularity; Carathéodory function PDFBibTeX XMLCite \textit{L. Esposito} and \textit{G. Mingione}, Rend. Mat. Appl., VII. Ser. 19, No. 1, 17--44 (1999; Zbl 0949.49023)