Local Morrey estimate in Musielak-Orlicz-Sobolev space

Abstract

Under appropriate assumptions on the $N(\Omega)$-fucntion, locally uniform Morrey estimate is presented in the Musielak-Orlicz-Sobolev space. The assumptions include a new increasing condition on the $x$-derivative of the Young complementary function of the $N(\Omega)$-fucntion. The conclusion applies to several important nonlinear examples frequently appeared in mathematical literature.