* Both the two- and three-dimensional versions of Ladyzhenskaya's inequality are special cases of the Gagliardo–Nirenberg interpolation inequality
:which holds whenever
:Ladyzhenskaya's inequalities are the special cases   when  and  when . 
* A simple modification of the argument used by Ladyzhenskaya in her 1958 paper (see e.g. Constantin & Seregin 2010) yields the following inequality for , valid for all :
* The usual Ladyzhenskaya inequality on , can be generalized (see McCormick & al. 2013) to use the weak  "norm" of  in place of the usual  norm: