Absence of Lavrentiev’s gap for anisotropic functionals
Michał Borowski, Iwona Chlebicka, Błażej Miasojedow · Nonlinear Analysis · 2024
We establish the absence of the Lavrentiev gap between Sobolev and smooth maps for a non-autonomous variational problem of a general structure, where the integrand is assumed to be controlled by a function which is convex and anisotropic with respect to the last variable. This fact follows from new results on fine approximation properties of the natural underlying unconventional function space. Scalar and vector-valued problems are studied.