International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 5, Pages 293-299

Extreme points and rotundity of Orlicz-Sobolev spaces

Shutao Chen,1 Changying Hu,1 and Charles Xuejin Zhao2

1Department of Mathematics, Harbin Normal University, Harbin 150080, China
2Department of Mathematics, Box 20047, Savannah State University, Savannah 31404, GA, USA

Received 28 February 2002

Copyright © 2002 Shutao Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is well known that Sobolev spaces have played essential roles in solving nonlinear partial differential equations. Orlicz-Sobolev spaces are generalized from Sobolev spaces. In this paper, we present sufficient and necessary conditions of extreme points of Orlicz-Sobolev spaces. A sufficient and necessary condition of rotundity of Orlicz-Sobolev spaces is obtained.