Extremal functions in Poincare-Sobolev inequalities for functions of bounded variation

Vincent Bouchez, Jean Van Schaftingen

If $\Omega \subset {\mathbb{R}}^n$ is a smooth bounded domain and $q\in (0,\frac{n}{n-1})$ we consider the Poincare-Sobolev inequality \[ c \Bigl(\int_Ω \abs{u}^\frac{n}{n-1}\Bigr)^{1-\frac{1}{n…