Existence and Regularity Results for Some Elliptic Equations with Degenerate Coercivity and Singular Quadratic Lower-Order Terms

2019 ◽  
Vol 16 (4) ◽  
Author(s):  
Rezak Souilah
2020 ◽  
Vol 10 (1) ◽  
pp. 301-310
Author(s):  
Weilin Zou ◽  
Xinxin Li

Abstract In this paper, we prove the existence and regularity of solutions of the homogeneous Dirichlet initial-boundary value problem for a class of degenerate elliptic equations with lower order terms. The results we obtained here, extend some existing ones of [2, 9, 11] in some sense.


2019 ◽  
Vol 69 (6) ◽  
pp. 1351-1366 ◽  
Author(s):  
Hocine Ayadi ◽  
Rezak Souilah

Abstract In this paper we prove some existence and regularity results for nonlinear unilateral problems with degenerate coercivity via the penalty method.


2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Aziz Bouhlal ◽  
Abderrahmane El Hachimi ◽  
Jaouad Igbida ◽  
El Mostafa Sadek ◽  
Hamad Talibi Alaoui

We investigate existence and regularity of solutions to unbounded elliptic problem whose simplest model is {-div[(1+uq)∇u]+u=γ∇u2/1+u1-q+f  in  Ω,  u=0  on  ∂Ω,}, where 0<q<1, γ>0 and f belongs to some appropriate Lebesgue space. We give assumptions on f with respect to q and γ to show the existence and regularity results for the solutions of previous equation.


2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xiaohua He ◽  
Shuibo Huang ◽  
Qiaoyu Tian ◽  
Yonglin Xu

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.


2017 ◽  
Vol 20 (01) ◽  
pp. 1750012 ◽  
Author(s):  
Nam Q. Le

We use the method of sliding paraboloids to establish a Harnack inequality for linear, degenerate and singular elliptic equation with unbounded lower order terms. The equations we consider include uniformly elliptic equations and linearized Monge–Ampère equations. Our argument allows us to prove the doubling estimate for functions which, at points of large gradient, are solutions of (degenerate and singular) elliptic equations with unbounded drift.


Sign in / Sign up

Export Citation Format

Share Document