scholarly journals The impact of a lower order term in a Dirichlet problem with a singular nonlinearity

2020 ◽  
Vol 76 (3) ◽  
pp. 407-415
Author(s):  
Lucio Boccardo ◽  
Gisella Croce
Keyword(s):  
Dirichlet Problem ◽  
Lower Order ◽  
Order Term ◽  
Lower Order Term ◽  
Singular Nonlinearity ◽  
The Impact

scholarly journals A regularity result for a class of elliptic equations with lower order terms

2020 ◽  
Vol 6 (2) ◽  
pp. 751-771 ◽  
Author(s):  
Claudia Capone ◽  
Teresa Radice
Keyword(s):  
Dirichlet Problem ◽  
Lower Order ◽  
Elliptic Equations ◽  
Order Term ◽  
Regularity Result ◽  
Lower Order Term ◽  
Bounded Solutions ◽  
Differentiability Of Solutions ◽  
Higher Differentiability ◽  
Lower Order Terms

Abstract In this paper we establish the higher differentiability of solutions to the Dirichlet problem $$\begin{aligned} {\left\{ \begin{array}{ll} \text {div} (A(x, Du)) + b(x)u(x)=f &{} \text {in}\, \Omega \\ u=0 &{} \text {on} \, \partial \Omega \end{array}\right. } \end{aligned}$$ div ( A ( x , D u ) ) + b ( x ) u ( x ) = f in Ω u = 0 on ∂ Ω under a Sobolev assumption on the partial map $$x \rightarrow A(x, \xi )$$ x → A ( x , ξ ) . The novelty here is that we take advantage from the regularizing effect of the lower order term to deal with bounded solutions.

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.

Elliptic equations with general singular lower order term and measure data

2015 ◽  
Vol 128 ◽  
pp. 391-411 ◽  
Author(s):  
Linda Maria De Cave ◽  
Francescantonio Oliva
Keyword(s):  
Lower Order ◽  
Elliptic Equations ◽  
Order Term ◽  
Lower Order Term ◽  
Measure Data
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