scholarly journals On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent

2018 ◽  
Vol 11 (3) ◽  
pp. 379-389 ◽  
Author(s):  
Anouar Bahrouni ◽  
◽  
VicenŢiu D. RĂdulescu ◽  
◽  
Keyword(s):  
Sobolev Space ◽  
Variable Exponent ◽  
Variational Problems ◽  
Fractional Sobolev Space

scholarly journals General fractional Sobolev space with variable exponent and applications to nonlocal problems

2020 ◽  
Vol 5 (4) ◽  
pp. 1512-1540 ◽  
Author(s):  
Elhoussine Azroul ◽  
Abdelmoujib Benkirane ◽  
Mohammed Shimi
Keyword(s):  
Sobolev Space ◽  
Variable Exponent ◽  
Nonlocal Problems ◽  
Fractional Sobolev Space

scholarly journals Generalization of Poincar ´e inequality in a Sobolev Space with exponent constant to the case of Sobolev space with a variable exponent

2021 ◽  
Vol 10 (2) ◽  
pp. 31-37
Author(s):  
Moulay Rchid Sidi Ammi ◽  
Ibrahim Dahi
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Poincaré Inequality ◽  
Poincare Inequality ◽  
Equivalent Norms

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).

scholarly journals Characterization of generalized Orlicz spaces

2018 ◽  
Vol 22 (02) ◽  
pp. 1850079 ◽  
Author(s):  
Rita Ferreira ◽  
Peter Hästö ◽  
Ana Margarida Ribeiro
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Orlicz Spaces ◽  
Difference Quotient ◽  
Variable Exponent Spaces ◽  
The Difference ◽  
Fractional Smoothness

The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz–Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.

scholarly journals Critical and subcritical fractional Trudinger–Moser-type inequalities on ℝ \mathbb{R}

2017 ◽  
Vol 8 (1) ◽  
pp. 868-884 ◽  
Author(s):  
Futoshi Takahashi
Keyword(s):  
Sobolev Space ◽  
Real Line ◽  
Fractional Sobolev Space

Abstract In this paper, we are concerned with the critical and subcritical Trudinger–Moser-type inequalities for functions in a fractional Sobolev space {H^{1/2,2}} on the whole real line. We prove the relation between two inequalities and discuss the attainability of the suprema.

scholarly journals Sobolev spaces and hyperbolic fillings

2018 ◽  
Vol 2018 (737) ◽  
pp. 161-187 ◽  
Author(s):  
Mario Bonk ◽  
Eero Saksman
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Measure Space ◽  
Weak Type ◽  
Poincaré Inequality ◽  
Metric Measure Space ◽  
Poincare Inequality ◽  
Fractional Sobolev Space ◽  
Gradient Condition

AbstractLetZbe an AhlforsQ-regular compact metric measure space, where{Q>0}. For{p>1}we introduce a new (fractional) Sobolev space{A^{p}(Z)}consisting of functions whose extensions to the hyperbolic filling ofZsatisfy a weak-type gradient condition. IfZsupports aQ-Poincaré inequality with{Q>1}, then{A^{Q}(Z)}coincides with the familiar (homogeneous) Hajłasz–Sobolev space.

Sign in / Sign up

Export Citation Format

Share Document