scholarly journals Attainability of the best Sobolev constant in a ball

2018 ◽  
Vol 375 (1-2) ◽  
pp. 1-16
Author(s):  
Norisuke Ioku
Keyword(s):  
Sobolev Constant

Multiple positive solutions of nonhomogeneous semilinear elliptic equations in ℝN

1996 ◽  
Vol 126 (2) ◽  
pp. 443-463 ◽  
Author(s):  
Cao Dao-Min ◽  
Zhou Huan-Song
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Multiple Positive Solutions ◽  
Semilinear Elliptic ◽  
Sobolev Constant ◽  
Image Position

We consider the following problemwhere for all ≦f(x,u)≦c1up-1 + c2u for all x ∈ℝN,u≧0 with c1>0,c2∈(0, 1), 2<p<(2N/(N – 2)) if N ≧ 3, 2 ≧ + ∝ if N = 2. We prove that (*) has at least two positive solutions ifand h≩0 in ℝN, where S is the best Sobolev constant and

The best sobolev constant

1992 ◽  
Vol 47 (1-4) ◽  
pp. 227-239 ◽  
Author(s):  
Charles A. Swanson
Keyword(s):  
Sobolev Constant

The Calabi flow on Kähler Surfaces with bounded Sobolev constant (I)

2011 ◽  
Vol 354 (1) ◽  
pp. 227-261 ◽  
Author(s):  
Xiuxiong Chen ◽  
Weiyong He
Keyword(s):  
Calabi Flow ◽  
Kähler Surfaces ◽  
Sobolev Constant

scholarly journals Two isoperimetric inequalities for the Sobolev constant

2012 ◽  
Vol 63 (5) ◽  
pp. 855-863 ◽  
Author(s):  
Tom Carroll ◽  
Jesse Ratzkin
Keyword(s):  
Isoperimetric Inequalities ◽  
Sobolev Constant
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