International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 5, Pages 293-299
doi:10.1155/S0161171202202252
Extreme points and rotundity of Orlicz-Sobolev spaces
Shutao Chen1
, Changying Hu1
and Charles Xuejin Zhao3
1Department of Mathematics, Harbin Normal University, Harbin 150080, China
3Department of Mathematics, Box 20047, Savannah State University, Savannah 31404, GA, USA
Abstract
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.