Uniform convexity of Musielak–Orlicz–Sobolev spaces and applications

This paper deals with uniform convexity of Musielak–Orlicz–Sobolev spaces and its applications to variational problems. Some sufficient conditions and examples for uniform convexity of Musielak–Orlicz–Sobolev spaces are given. Some special properties relative to the uniformly convex modular for uniformly convex Musielak–Orlicz–Sobolev spaces are presented. As an application of these abstract results, the local minimizers and the mountain pass type critical point of an integral functional with more complicated growth than the p(x)p(x)-growth are studied.