scholarly journals Weighted Poincaré inequality and the Poisson Equation

2020 ◽  
pp. 1
Author(s):  
Ovidiu Munteanu ◽  
Chiung-Jue Anna Sung ◽  
Jiaping Wang
Keyword(s):  
Poisson Equation ◽  
Poincaré Inequality ◽  
Poincare Inequality ◽  
The Poisson Equation ◽  
Weighted Poincaré Inequality

scholarly journals Vanishing theorems on complete manifolds with weighted Poincaré inequality and applications

2012 ◽  
Vol 206 ◽  
pp. 25-37
Author(s):  
Hai-Ping Fu ◽  
Deng-Yun Yang
Keyword(s):  
Harmonic Map ◽  
Poincaré Inequality ◽  
Vanishing Theorems ◽  
Poincare Inequality ◽  
Noncompact Manifolds ◽  
Weighted Poincaré Inequality ◽  
Complete Manifolds

AbstractTwo vanishing theorems for harmonic map andL2harmonic 1-form on complete noncompact manifolds are proved under certain geometric assumptions, which generalize results of [13], [15], [18], [19], and [20]. As applications, we improve some main results in [2], [4], [6], [9], [12], [20], [22], [24], and [25].

On Weighted Sobolev Spaces

1996 ◽  
Vol 48 (3) ◽  
pp. 527-541 ◽  
Author(s):  
Seng-Kee Chua
Keyword(s):  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Poincaré Inequality ◽  
Poincare Inequality ◽  
Extension Theorems ◽  
Doubling Weight ◽  
Weighted Poincaré Inequality

AbstractWe study density and extension problems for weighted Sobolev spaces on bounded (ε, δ) domains𝓓when a doubling weight w satisfies the weighted Poincaré inequality on cubes near the boundary of 𝓓 and when it is in the MuckenhouptApclass locally in 𝓓. Moreover, when the weightswi(x) are of the form dist(x,Mi)αi,αi∈ ℝ,Mi⊂ 𝓓that are doubling, we are able to obtain some extension theorems on (ε, ∞) domains.

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