Remarks on the Uniqueness of a Solution of the Dirichlet Problem for Second-Order Elliptic Equations with Lower-Order Terms

2004 ◽  
Vol 38 (3) ◽  
pp. 173-183 ◽  
Author(s):  
V. V. Zhikov
Keyword(s):  
Dirichlet Problem ◽  
Lower Order ◽  
Elliptic Equations ◽  
Second Order ◽  
Second Order Elliptic Equations ◽  
Lower Order Terms ◽  
Uniqueness Of A Solution

scholarly journals Existence of Solutions to Elliptic Problem with Convection Term and Lower-Order Term

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xiaohua He ◽  
Shuibo Huang ◽  
Qiaoyu Tian ◽  
Yonglin Xu
Keyword(s):  
Dirichlet Problem ◽  
Lower Order ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Order Term ◽  
Combined Effects ◽  
Convection Term ◽  
Bounded Smooth Domain ◽  
Bounded Smooth ◽  
Lower Order Terms

In this paper, we establish the existence of solutions to the following noncoercivity Dirichlet problem − div M x ∇ u + u p − 1 u = − div u E x + f x , x ∈ Ω , u x = 0 , x ∈ ∂ Ω , where Ω ⊂ ℝ N N > 2 is a bounded smooth domain with 0 ∈ Ω , f belongs to the Lebesgue space L m Ω with m ≥ 1 , p > 0 . The main innovation point of this paper is the combined effects of the convection terms and lower-order terms in elliptic equations.

On Dirichlet problem for second order elliptic equations

1990 ◽  
Vol 14 (7) ◽  
pp. 559-570 ◽  
Author(s):  
A. Alvino ◽  
P. Buonocore ◽  
G. Trombetti
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Second Order ◽  
Second Order Elliptic Equations
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