Local Morrey estimate in Musielak-Orlicz-Sobolev space - Liu, Duchao; Zhao, Peihao (Topological Methods in Nonlinear Analysis, 2023)
Under appropriate assumptions on the N(Ω)-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(Ω)-fucntion. The conclusion applies to several important nonlinear examples frequently appeared in mathematical literature.