  This pre-print has now been superseded by arXiv:2305.19934 and will not be
published.
  We prove that for convex vectorial functionals with (p,q)-growth the
Lavrentiev phenomenon does not occur up to the boundary when (p,q) are suitably
restricted. Under minimal assumptions on the regularity of the domain and the
boundary data, we obtain results for autonomous and non-autonomous functionals,
under natural, controlled and controlled duality growth bounds.
