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The nonoccurrence of the Lavrentiev phenomenon for a class of variational functionals. (English) Zbl 1268.49020

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.

MSC:

49K10 Optimality conditions for free problems in two or more independent variables
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