scholarly journals A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces.

Author(s):  
Petteri Harjulehto ◽  
Peter Hästö
2021 ◽  
Vol 10 (2) ◽  
pp. 31-37
Author(s):  
Moulay Rchid Sidi Ammi ◽  
Ibrahim Dahi

In this work, we study the Poincare inequality in Sobolev spaces with variable exponent. As a consequence of this ´ result we show the equivalent norms over such cones. The approach we adopt in this work avoids the difficulty arising from the possible lack of density of the space C∞ 0 (Ω).


2006 ◽  
Vol 36 (0) ◽  
pp. 79-94 ◽  
Author(s):  
Petteri Harjulehto ◽  
Peter Hästö ◽  
Mikko Pere

2015 ◽  
Vol 127 ◽  
pp. 196-205 ◽  
Author(s):  
Thanasis Kostopoulos ◽  
Nikos Yannakakis

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Toni Heikkinen

Let Φ be anN-function. We show that a functionu∈LΦ(ℝn)belongs to the Orlicz-Sobolev spaceW1,Φ(ℝn)if and only if it satisfies the (generalized) Φ-Poincaré inequality. Under more restrictive assumptions on Φ, an analog of the result holds in a general metric measure space setting.


2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Yongqiang Fu ◽  
Miaomiao Yang

This paper is concerned with the functionalJdefined byJ(u)=∫Ω×ΩW(x,y,∇u(x),∇u(y))dx dy, whereΩ⊂ℝNis a regular open bounded set andWis a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicontinuity and relaxation ofJ.


2013 ◽  
Vol 218 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Katarzyna Pietruska-Pałuba ◽  
Andrzej Stós

2006 ◽  
Vol 58 (3) ◽  
pp. 492-528 ◽  
Author(s):  
Seng-Kee Chua

AbstractWe extend the extension theorems to weighted Sobolev spaces on (ε, δ) domains with doubling weight w that satisfies a Poincaré inequality and such that w–1/p is locally Lp′. We also make use of the main theorem to improve weighted Sobolev interpolation inequalities.


Author(s):  
Przemysław Górka ◽  
Nijjwal Karak ◽  
Daniel J. Pons

2001 ◽  
Vol 185 (2) ◽  
pp. 527-563 ◽  
Author(s):  
Fuzhou Gong ◽  
Michael Röckner ◽  
Wu Liming

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