Let $\Omega \subset \mathbb{R}^n$ be a bounded Lipschitz set, and let $W^{k,p}(\Omega)$ denote the usual Sobolev space with $k \in \mathbb{N}$ being the order of the derivatives and $p \in [1, \infty)$ the rate of integrability. I know that there exists a result of this type: fix $\varepsilon >0$, then $$\Vert f\Vert_{W^{k-1,p}(\Omega)} \leq \varepsilon \Vert f\Vert_{W^{k,p}(\Omega)} + c(\varepsilon) \Vert f\Vert_{L^1(\Omega)}$$ for any function $f \in W^{k-1,p}(\Omega)$, where the constant $c(\varepsilon)>0$ depends on $\varepsilon$ but not on $f \in W^{k-1,p}(\Omega)$.

Do you know how to prove it, or have any reference to a book/paper where I can find the proof of this result?