scholarly journals Continuity of Sobolev functions of variable exponent on metric spaces

2004 ◽  
Vol 80 (6) ◽  
pp. 96-99 ◽  
Author(s):  
Yoshihiro Mizuta ◽  
Tetsu Shimomura
2017 ◽  
Vol 67 (1) ◽  
pp. 199-208
Author(s):  
Michał Gaczkowski ◽  
Przemysław Górka

Abstract We study variable exponent Sobolev spaces on compact metric spaces. Without the assumption of log-Hölder continuity of the exponent, the compact Sobolev-type embeddings theorems for these spaces are shown.


2007 ◽  
Vol 59 (6) ◽  
pp. 1135-1153 ◽  
Author(s):  
Anders Björn ◽  
Jana Björn ◽  
Nageswari Shanmugalingam

AbstractWe study when characteristic and Hölder continuous functions are traces of Sobolev functions on doubling metric measure spaces. We provide analytic and geometric conditions sufficient for extending characteristic and Hölder continuous functions into globally defined Sobolev functions.


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