International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 5, Pages 293-299
Extreme points and rotundity of Orlicz-Sobolev spaces
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.