On global absence of Lavrentiev gap for functionals with (p,q)-growth

Lukas Koch

Published 2022-10-27Version 1

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.