Bonfanti, Giovanni; Cellina, Arrigo The nonoccurrence of the Lavrentiev phenomenon for a class of variational functionals. (English) Zbl 1268.49020 SIAM J. Control Optim. 51, No. 2, 1639-1650 (2013). Summary: We prove that the Lavrentiev phenomenon does not occur for the functional \(\int_{\Omega} [l(|\nabla u(x)|)+ G(u)] dx\) on \(u-u^0\in W^{1,1}_0(\Omega)\), where \(L\) and \(G\) are convex functions subject to additional regularity assumptions, and where \(\partial \Omega\) and \(u^0\) are smooth. Cited in 6 Documents MSC: 49K10 Optimality conditions for free problems in two or more independent variables Keywords:calculus of variations; Lavrentiev phenomenon; boundedness of solutions PDFBibTeX XMLCite \textit{G. Bonfanti} and \textit{A. Cellina}, SIAM J. Control Optim. 51, No. 2, 1639--1650 (2013; Zbl 1268.49020) Full Text: DOI