scholarly journals The variable exponent Sobolev capacity and quasi-fine properties of Sobolev functions in the casep−=1

2014 ◽  
Vol 412 (1) ◽  
pp. 168-180
Author(s):  
Heikki Hakkarainen ◽  
Matti Nuortio
Keyword(s):  
Variable Exponent ◽  
Sobolev Functions ◽  
Sobolev Capacity

scholarly journals The variable exponent BV-Sobolev capacity

2012 ◽  
Vol 27 (1) ◽  
pp. 13-40 ◽  
Author(s):  
Heikki Hakkarainen ◽  
Matti Nuortio
Keyword(s):  
Variable Exponent ◽  
Sobolev Capacity

scholarly journals Sobolev capacity on the spaceW1, p(⋅)(ℝn)

2003 ◽  
Vol 1 (1) ◽  
pp. 17-33 ◽  
Author(s):  
Petteri Harjulehto ◽  
Peter Hästö ◽  
Mika Koskenoja ◽  
Susanna Varonen
Keyword(s):  
Hausdorff Dimension ◽  
Sobolev Space ◽  
Variable Exponent ◽  
Choquet Capacity ◽  
Sobolev Capacity

We define Sobolev capacity on the generalized Sobolev spaceW1, p(⋅)(ℝn). It is a Choquet capacity provided that the variable exponentp:ℝn→[1,∞)is bounded away from 1 and∞. We discuss the relation between the Hausdorff dimension and the Sobolev capacity. As another application we study quasicontinuous representatives in the spaceW1, p(⋅)(ℝn).

EMBEDDING AND TRACE RESULTS FOR VARIABLE EXPONENT SOBOLEV AND MAZ'YA SPACES ON NON-SMOOTH DOMAINS

2015 ◽  
Vol 58 (2) ◽  
pp. 471-489 ◽  
Author(s):  
ALEJANDRO VÉLEZ-SANTIAGO
Keyword(s):  
Sobolev Spaces ◽  
Variable Exponent ◽  
Linear Equations ◽  
Well Posedness ◽  
Variable Exponent Sobolev Spaces ◽  
Sobolev Functions

AbstractWe establish interior and trace embedding results for Sobolev functions on a class of bounded non-smooth domains. Also, we define the corresponding generalized Maz'ya spaces of variable exponent, and obtain embedding results similar as in the constant case. Some relations between the variable exponent Maz'ya spaces and the variable exponent Sobolev spaces are also achieved. At the end, we give an application of the previous results for the well-posedness of a class of quasi-linear equations with variable exponent.

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