Local Morrey estimate in Musielak-Orlicz-Sobolev space

Abstract

Under appropriate assumptions on the $N(\Omega )$-fucntion, 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.

12 pages. arXiv admin note: text overlap with arXiv:1805.11469, arXiv:1711.11229