scholarly journals On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications

2008 ◽  
Vol 14 (2) ◽  
pp. 211-232 ◽  
Author(s):  
Lars Diening ◽  
Josef Málek ◽  
Mark Steinhauer
Keyword(s):  
Variable Exponent ◽  
Sobolev Functions

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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