scholarly journals Higher order weighted Sobolev spaces on the real line for strongly degenerate weights. Application to variational problems in elasticity of beams

2020 ◽  
Vol 488 (1) ◽  
pp. 124038
Author(s):  
Karol Bołbotowski
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Weighted Sobolev Spaces ◽  
Variational Problems ◽  
Higher Order ◽  
The Real ◽  
Strongly Degenerate

A duality principle in weighted Sobolev spaces on the real line

2015 ◽  
Vol 288 (8-9) ◽  
pp. 877-897 ◽  
Author(s):  
Simon P. Eveson ◽  
Vladimir D. Stepanov ◽  
Elena P. Ushakova
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Weighted Sobolev Spaces ◽  
Duality Principle ◽  
The Real

Associated Spaces to Weighted Sobolev Spaces on the Real Line

2018 ◽  
Vol 481 (5) ◽  
pp. 486-489 ◽  
Author(s):  
D. Prokhorov ◽  
◽  
V. Stepanov ◽  
E. Ushakova ◽  
◽  
...  
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Weighted Sobolev Spaces ◽  
The Real ◽  
Associated Spaces

Spaces Associated with Weighted Sobolev Spaces on the Real Line

2018 ◽  
Vol 98 (1) ◽  
pp. 373-376 ◽  
Author(s):  
D. V. Prokhorov ◽  
V. D. Stepanov ◽  
E. P. Ushakova
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Weighted Sobolev Spaces ◽  
The Real

On weighted Sobolev spaces on the real line

2016 ◽  
Vol 93 (1) ◽  
pp. 78-81 ◽  
Author(s):  
D. V. Prokhorov ◽  
V. D. Stepanov ◽  
E. P. Ushakova
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Weighted Sobolev Spaces ◽  
The Real

scholarly journals Higher Order Sobolev-Type Spaces on the Real Line

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Bogdan Bojarski ◽  
Juha Kinnunen ◽  
Thomas Zürcher
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Finite Differences ◽  
Higher Order ◽  
Sobolev Type ◽  
The Real ◽  
Sobolev Functions ◽  
Sobolev Type Spaces ◽  
Type Spaces

This paper gives a characterization of Sobolev functions on the real line by means of pointwise inequalities involving finite differences. This is also shown to apply to more general Orlicz-Sobolev, Lorentz-Sobolev, and Lorentz-Karamata-Sobolev spaces.

scholarly journals Multiple solutions for some strongly degenerate second order elliptic equations

2021 ◽  
pp. 1-12
Author(s):  
João R. Santos ◽  
Gaetano Siciliano
Keyword(s):  
Boundary Value Problem ◽  
Bounded Domain ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Existence Of Solutions ◽  
Weighted Sobolev Spaces ◽  
Degenerate Operator ◽  
Second Order Elliptic Equations ◽  
Strongly Degenerate

We consider a boundary value problem in a bounded domain involving a degenerate operator of the form L ( u ) = − div ( a ( x ) ∇ u ) and a suitable nonlinearity f. The function a vanishes on smooth 1-codimensional submanifolds of Ω where it is not allowed to be C 2 . By using weighted Sobolev spaces we are still able to find existence of solutions which vanish, in the trace sense, on the set where a vanishes.

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