On relative compactness of a set of abstract functions in a scale of Banach spaces

1992 ◽  
Vol 34 (2) ◽  
pp. 320-329
Author(s):  
A. G. Podgaev
Keyword(s):  
Banach Spaces ◽  
Relative Compactness ◽  
Scale Of Banach Spaces

scholarly journals An Application Of The Theory Of Scale Of Banach Spaces

2015 ◽  
Vol 29 (1) ◽  
pp. 51-59
Author(s):  
Łukasz Dawidowski
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Banach Spaces ◽  
Abstract Cauchy Problem ◽  
Initial Boundary ◽  
Scale Of Banach Spaces ◽  
The Cauchy Problem ◽  
Selection Of

AbstractThe abstract Cauchy problem on scales of Banach space was considered by many authors. The goal of this paper is to show that the choice of the space on scale is significant. We prove a theorem that the selection of the spaces in which the Cauchy problem ut − Δu = u|u|s with initial–boundary conditions is considered has an influence on the selection of index s. For the Cauchy problem connected with the heat equation we will study how the change of the base space influents the regularity of the solutions.

Sobolev problem in the complete scale of Banach Spaces

1996 ◽  
Vol 48 (11) ◽  
pp. 1758-1767 ◽  
Author(s):  
Ya. A. Roitberg ◽  
A. V. Sklyarets
Keyword(s):  
Banach Spaces ◽  
Sobolev Problem ◽  
Scale Of Banach Spaces

On the Sobolev problem in the complete scale of Banach spaces

1999 ◽  
Vol 51 (9) ◽  
pp. 1330-1342
Author(s):  
V. N. Los' ◽  
Ya. A. Roitberg
Keyword(s):  
Banach Spaces ◽  
Sobolev Problem ◽  
Scale Of Banach Spaces
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