Discarding Lavrentiev's Gap in Non-autonomous and Non-Convex Variational Problems

Michał Borowski, Pierre Bousquet, Iwona Chlebicka +2

We establish that the Lavrentiev gap between Sobolev and Lipschitz maps does not occur for a scalar variational problem of the form: \[ \textrm{to minimize} \qquad u \mapsto \int_Î…