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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.

The Nonoccurrence of the Lavrentiev Phenomenon for a Class of Variational Functionals