scholarly journals Sharp Constants of Brézis-Gallouët-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin Spaces

2010 ◽  
Vol 2010 (1) ◽  
pp. 584521 ◽  
Author(s):  
Kei Morii ◽  
Tokushi Sato ◽  
Yoshihiro Sawano ◽  
Hidemitsu Wadade
Keyword(s):  
Bounded Domains ◽  
Sharp Constants ◽  
Logarithmic Term

SOME -HARDY AND -RELLICH TYPE INEQUALITIES WITH REMAINDER TERMS

2021 ◽  
pp. 1-20
Author(s):  
YONGYANG JIN ◽  
SHOUFENG SHEN
Keyword(s):  
Riemannian Manifolds ◽  
Bounded Domains ◽  
Hadamard Manifolds ◽  
Sharp Constants ◽  
Hyperbolic Functions

Abstract In this paper we obtain some improved $L^p$ -Hardy and $L^p$ -Rellich inequalities on bounded domains of Riemannian manifolds. For Cartan–Hadamard manifolds we prove the inequalities with sharp constants and with weights being hyperbolic functions of the Riemannian distance.

Fractional abstract Cauchy problem on complex interpolation scales

2020 ◽  
Vol 23 (4) ◽  
pp. 1125-1140
Author(s):  
Andriy Lopushansky ◽  
Oleh Lopushansky ◽  
Anna Szpila
Keyword(s):  
Cauchy Problem ◽  
Time Derivative ◽  
Abstract Cauchy Problem ◽  
Initial Boundary ◽  
Sectorial Operator ◽  
Complex Interpolation ◽  
Bounded Domains ◽  
Initial Boundary Value Problems ◽  
Fractional Time Derivative ◽  
Initial Boundary Value

AbstractAn fractional abstract Cauchy problem generated by a sectorial operator is investigated. An inequality of coercivity type for its solution with respect to a complex interpolation scale generated by a sectorial operator with the same parameters is established. An application to differential parabolic initial-boundary value problems in bounded domains with a fractional time derivative is shown.

Sign in / Sign up

Export Citation Format

Share Document