Nonoccurrence of the Lavrentiev phenomenon for many nonconvex constrained variational problems (Q866979)

A complete metric space \({\mathcal M}\) of functions, which satisfy a growth condition common in the literature and are Lipschitzian on bounded sets, is considered. The nonoccurrence of the Lavrentiev phenomenon for most elements of \({\mathcal M}\), in the sense of Baire category, is established.