Uniform convexity of Musielak–Orlicz–Sobolev spaces and applications

By Xianling Fan, Chunxia Guan. 2010

56 citations recorded by the source corpus.

Abstract 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 ) -growth are studied.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/910079d2eeee871a108dc2b2cfe080a540dd629b

Citations in the corpus

• A new class of double phase variable exponent problems: Existence and uniqueness (2021, unknown): “Thus (ii) follows from Theorem 3.5 of Fan-Guan [30].”