Generalized Sobolev spaces and their application to boundary problems for partial differential equations

1966 ◽  
pp. 207-275 ◽  
Author(s):  
L. N. Slobodeckiĭ
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Sobolev Spaces ◽  
Partial Differential ◽  
Boundary Problems ◽  
Generalized Sobolev Spaces

scholarly journals On Babinet's Principle

1958 ◽  
Vol 10 ◽  
pp. 632-640 ◽  
Author(s):  
R. C. MacCamy
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Electromagnetic Theory ◽  
Partial Differential ◽  
Boundary Problems ◽  
Plane Obstacle ◽  
Equivalent Boundary

In acoustic and electromagnetic theory much use is made of what is called the Principle of Babinet (1). The principle states that the problems of diffraction by an aperture, S, in a plane screen and by a plane obstacle occupying the position S, are equivalent. It is the intent of this paper to indicate how this notion of equivalent boundary problems, for partial differential equations, can be extended to other situations.

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.

Sign in / Sign up

Export Citation Format

Share Document