Boundary Behavior of Monotone Sobolev Functions in Orlicz Spaces on John Domains in a Metric Space

2017 ◽  
Vol 28 (2) ◽  
pp. 1233-1244 ◽  
Author(s):  
Toshihide Futamura ◽  
Tetsu Shimomura
Keyword(s):  
Metric Space ◽  
Boundary Behavior ◽  
Orlicz Spaces ◽  
Sobolev Functions ◽  
John Domains ◽  
Monotone Sobolev Functions

scholarly journals Lindelöf theorems for monotone Sobolev functions in Orlicz spaces

2013 ◽  
Vol 57 (4) ◽  
pp. 1025-1033 ◽  
Author(s):  
Fausto Di Biase ◽  
Toshihide Futamura ◽  
Tetsu Shimomura
Keyword(s):  
Orlicz Spaces ◽  
Sobolev Functions ◽  
Monotone Sobolev Functions

The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph

2016 ◽  
Vol 59 (01) ◽  
pp. 3-12 ◽  
Author(s):  
Monther Rashed Alfuraidan
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Orlicz Spaces ◽  
Multivalued Mappings ◽  
Linear Spaces ◽  
Modular Metric Spaces ◽  
Modular Spaces

Abstract We study the existence of fixed points for contraction multivalued mappings in modular metric spaces endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as a generalization of Nadler and Edelstein’s fixed point theorems to modular metric spaces endowed with a graph.

scholarly journals Sharp Exponential Integrability for Traces of Monotone Sobolev Functions

2008 ◽  
Vol 192 ◽  
pp. 137-149 ◽  
Author(s):  
Pekka Pankka ◽  
Pietro Poggi-Corradini ◽  
Kai Rajala
Keyword(s):  
Unit Ball ◽  
Exponential Integrability ◽  
Geometric Methods ◽  
Sobolev Functions ◽  
Integrability Of Functions ◽  
Monotone Sobolev Functions

AbstractWe answer a question posed in [12] on exponential integrability of functions of restricted n-energy. We use geometric methods to obtain a sharp exponential integrability result for boundary traces of monotone Sobolev functions defined on the unit ball.

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