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
Keyword(s):  
Variable Exponent ◽  
Metric Spaces ◽  
Sobolev Functions

Variable Hajłasz-Sobolev spaces on compact metric spaces

2017 ◽  
Vol 67 (1) ◽  
pp. 199-208
Author(s):  
Michał Gaczkowski ◽  
Przemysław Górka
Keyword(s):  
Sobolev Spaces ◽  
Variable Exponent ◽  
Metric Spaces ◽  
Hölder Continuity ◽  
Sobolev Type ◽  
Holder Continuity ◽  
Study Variable ◽  
Compact Metric Spaces ◽  
Variable Exponent Sobolev Spaces

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.

Sobolev Extensions of Hölder Continuous and Characteristic Functions on Metric Spaces

2007 ◽  
Vol 59 (6) ◽  
pp. 1135-1153 ◽  
Author(s):  
Anders Björn ◽  
Jana Björn ◽  
Nageswari Shanmugalingam
Keyword(s):  
Metric Spaces ◽  
Continuous Functions ◽  
Characteristic Functions ◽  
Metric Measure Spaces ◽  
Hölder Continuous ◽  
Geometric Conditions ◽  
Sobolev Functions ◽  
Measure Spaces ◽  
Hölder Continuous Functions

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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