A Gagliardo-Nirenberg inequality, with application to duality-based a posteriori error estimation in the L1 norm

We establish the Gagliardo-Nirenberg-type multiplicative interpolation inequality $ \[ \|v\|_{{\rm L}1(\mathbb{R}^n)} \leq C \|v\|^{1/2}_{{\rm Lip}'(\mathbb{R}^n)} \|v\|^{1/2}_{{\rm BV}(\mathbb{R}^n)}\qquad \forall v \in {\rm BV}(\mathbb{R}^n), \] $ where $C$ is a positive constant, independent...