On the Lavrentiev gap for convex, vectorial integral functionals

Lukas Koch, Matthias Ruf, Mathias Schäffner

We prove the absence of a Lavrentiev gap for vectorial integral functionals of the form $$ F: g+W_0^{1,1}(Ω)^m\to\mathbb{R}\cup\{+\infty\},\qquad F(u)=\int_ΩW(x,\mathrm{D} u)\,\m…