Interpolation inequalities for derivatives in Orlicz spaces Agnieszka KalamajskaKatarzyna Pietruska-Paluba We prove variants of the classical Gagliardo-Nirenberg inequalities in both additive and multiplicative forms, with Orlicz norms replacing the usual $L^{p}$ norms. The $N$-functions involved satisfy certain consistency conditions. We also prove more general interpolation inequalities for derivatives, where the Orlicz norm of $|\nabla u|$ is estimated by the Orlicz norms of expressions of the form $\Psi(|u|, |\nabla^{(2)}u|)$. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2825 10.1512/iumj.2006.55.2825 en Indiana Univ. Math. J. 55 (2006) 1767 - 1790 state-of-the-art mathematics http://iumj.org/access/