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

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

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.

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 The Cauchy problem in scale of Banach spaces with deviating variables

2021 ◽  
Vol 22 (1) ◽  
pp. 219-230
Author(s):  
Nguyen Bich Huy ◽  
Pham Van Hien
Keyword(s):  
Cauchy Problem ◽  
Banach Spaces ◽  
Scale Of Banach Spaces ◽  
The Cauchy Problem

scholarly journals A fixed point theorem and an application for the Cauchy problem in the scale of Banach spaces

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4387-4398 ◽  
Author(s):  
Vo Tri ◽  
Erdal Karapinar
Keyword(s):  
Cauchy Problem ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Convex Space ◽  
Locally Convex Space ◽  
Normed Spaces ◽  
Scale Of Banach Spaces ◽  
The Cauchy Problem ◽  
Locally Convex

The main aim of this paper is to prove the existence of the fixed point of the sum of two operators in setting of the cone-normed spaces with the values of cone-norm belonging to an ordered locally convex space. We apply this result to prove the existence of global solution of the Cauchy problem with perturbation of the form (x?(t) = f[t,x(t)] + g[t,x(t)], t ? [0,?), x(0) = x0? F1, in a scale of Banach spaces {(Fs,||.||) : s ? (0, 1]}.

Sobolev’s Problem in Complete Scale of Banach Spaces

2000 ◽  
pp. 301-312
Author(s):  
Yakov Roitberg ◽  
Valerii Los ◽  
Andrei Sklyarets
Keyword(s):  
Banach Spaces ◽  
Scale Of Banach Spaces
Sign in / Sign up

Export Citation Format

Share Document