Necessary conditions for optimality of singular controls in systems governed by partial differential equations

1984 ◽  
Vol 43 (4) ◽  
pp. 639-661 ◽  
Author(s):  
M. A. Kazemi-Dehkordi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Necessary Conditions ◽  
Partial Differential ◽  
Singular Controls ◽  
Necessary Conditions For Optimality

scholarly journals Extreme points and rotundity of Orlicz-Sobolev spaces

2002 ◽  
Vol 32 (5) ◽  
pp. 293-299
Author(s):  
Shutao Chen ◽  
Changying Hu ◽  
Charles Xuejin Zhao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Sobolev Spaces ◽  
Necessary Conditions ◽  
Nonlinear Partial Differential Equations ◽  
Extreme Points ◽  
Necessary Condition ◽  
Partial Differential ◽  
Sufficient And Necessary Conditions ◽  
Sufficient And Necessary Condition

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.

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