On the Best Constant in a Poincare-Sobolev Inequality

2000 ◽  
pp. 101-109
Author(s):  
Yuri V. Egorov
Keyword(s):  
Sobolev Inequality ◽  
Best Constant

On the best constant in a Hardy–Sobolev inequality

2006 ◽  
Vol 85 (1-3) ◽  
pp. 171-180 ◽  
Author(s):  
Angelo Alvino ◽  
Vincenzo Ferone ◽  
Guido Trombetti
Keyword(s):  
Sobolev Inequality ◽  
Best Constant

scholarly journals Fractional Hardy–Sobolev Inequalities with Magnetic Fields

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Min Liu ◽  
Fengli Jiang ◽  
Zhenyu Guo
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Sobolev Inequality ◽  
Sobolev Inequalities ◽  
Best Constant

A fractional Hardy–Sobolev inequality with a magnetic field is studied in the present paper. Under appropriate conditions, the achievement of the best constant of the fractional magnetic Hardy–Sobolev inequality is established.

scholarly journals The Best Constant of Discrete Sobolev Inequality on the C60 Fullerene Buckyball

2015 ◽  
Vol 84 (7) ◽  
pp. 074004 ◽  
Author(s):  
Yoshinori Kametaka ◽  
Atsushi Nagai ◽  
Hiroyuki Yamagishi ◽  
Kazuo Takemura ◽  
Kohtaro Watanabe
Keyword(s):  
Sobolev Inequality ◽  
C60 Fullerene ◽  
Best Constant

scholarly journals The Best Constant of Sobolev Inequality Corresponding to Clamped Boundary Value Problem

2011 ◽  
Vol 2011 (1) ◽  
Author(s):  
Kohtaro Watanabe ◽  
Yoshinori Kametaka ◽  
Hiroyuki Yamagishi ◽  
Atsushi Nagai ◽  
Kazuo Takemura
Keyword(s):  
Boundary Value Problem ◽  
Sobolev Inequality ◽  
Boundary Value ◽  
Best Constant

scholarly journals Symmetrization of Functions and the Best Constant of 1-DIM Sobolev Inequality

2009 ◽  
Vol 2009 (1) ◽  
pp. 874631 ◽  
Author(s):  
Kohtaro Watanabe ◽  
Yoshinori Kametaka ◽  
Atsushi Nagai ◽  
Hiroyuki Yamagishi ◽  
Kazuo Takemura
Keyword(s):  
Sobolev Inequality ◽  
Best Constant

Role of the fundamental solution in Hardy—Sobolev-type inequalities

2006 ◽  
Vol 136 (6) ◽  
pp. 1111-1130 ◽  
Author(s):  
Adimurthi ◽  
Anusha Sekar
Keyword(s):  
Fundamental Solution ◽  
Heisenberg Group ◽  
Sobolev Inequality ◽  
Fundamental Solutions ◽  
Sobolev Type ◽  
Best Constant ◽  
Optimal Estimates ◽  
Image Position

Let n ≥ 3, Ω ⊂ Rn be a domain with 0 ∈ Ω, then, for all the Hardy–Sobolev inequality says that and equality holds if and only if u = 0 and ((n − 2)/2)2 is the best constant which is never achieved. In view of this, there is scope for improving this inequality further. In this paper we have investigated this problem by using the fundamental solutions and have obtained the optimal estimates. Furthermore, we have shown that this technique is used to obtain the Hardy–Sobolev type inequalities on manifolds and also on the Heisenberg group.

scholarly journals The best constant of Sobolev inequality on a bounded interval

2008 ◽  
Vol 340 (1) ◽  
pp. 699-706 ◽  
Author(s):  
K. Watanabe ◽  
Y. Kametaka ◽  
A. Nagai ◽  
K. Takemura ◽  
H. Yamagishi
Keyword(s):  
Sobolev Inequality ◽  
Best Constant ◽  
Bounded Interval
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