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 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

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.