scholarly journals Existence and Regularity of Solutions for Unbounded Elliptic Equations with Singular Nonlinearities

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Aziz Bouhlal ◽  
Jaouad Igbida
Keyword(s):  
Elliptic Equations ◽  
Elliptic Problems ◽  
Regularity Of Solutions ◽  
Singular Nonlinearities

For q , γ > 0 , we study existence and regularity of solutions for unbounded elliptic problems whose simplest model is − div 1 + u q ∇ u = f / u γ in  Ω u = 0 on  ∂ Ω , where f ∈ L m Ω , m ≥ 1 .

scholarly journals Existence results for nonlinear degenerate elliptic equations with lower order terms

2020 ◽  
Vol 10 (1) ◽  
pp. 301-310
Author(s):  
Weilin Zou ◽  
Xinxin Li
Keyword(s):  
Lower Order ◽  
Elliptic Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Regularity Of Solutions ◽  
Degenerate Elliptic Equations ◽  
Degenerate Elliptic ◽  
Initial Boundary Value ◽  
Lower Order Terms ◽  
Nonlinear Degenerate

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.

Existence of Radial Solutions for Quasilinear Elliptic Equations with Singular Nonlinearities

2003 ◽  
Vol 3 (4) ◽  
Author(s):  
Beatrice Acciaio ◽  
Patrizia Pucci
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Quasilinear Elliptic Equations ◽  
Radial Solutions ◽  
Singular Nonlinearities ◽  
Quasilinear Elliptic

AbstractWe prove the existence of radial solutions of the quasilinear elliptic equation div(A(|Du|)Du) + f(u) = 0 in ℝ

scholarly journals Positive Solutions for Elliptic Problems with the Nonlinearity Containing Singularity and Hardy-Sobolev Exponents

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yong-Yi Lan ◽  
Xian Hu ◽  
Bi-Yun Tang
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Elliptic Problems ◽  
Semilinear Elliptic Equations ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions

In this paper, we study multiplicity of positive solutions for a class of semilinear elliptic equations with the nonlinearity containing singularity and Hardy-Sobolev exponents. Using variational methods, we establish the existence and multiplicity of positive solutions for the problem.

scholarly journals Existence of Solutions for Unbounded Elliptic Equations with Critical Natural Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Aziz Bouhlal ◽  
Abderrahmane El Hachimi ◽  
Jaouad Igbida ◽  
El Mostafa Sadek ◽  
Hamad Talibi Alaoui
Keyword(s):  
Elliptic Problem ◽  
Lebesgue Space ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Regularity Of Solutions ◽  
Natural Growth ◽  
Existence And Regularity Results ◽  
Regularity Results

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.

Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ3. Part II: Regularity in neighbourhoods of edges

1997 ◽  
Vol 127 (3) ◽  
pp. 517-545 ◽  
Author(s):  
Benqi Guo ◽  
Ivo Babuška
Keyword(s):  
Finite Elements ◽  
Weighted Sobolev Spaces ◽  
Elliptic Problems ◽  
Regularity Of Solutions ◽  
Normed Spaces ◽  
Qualitative And Quantitative ◽  
The Poisson Equation ◽  
Nonsmooth Domains ◽  
Polyhedral Domain ◽  
Derivatives Of

This paper is the second in a series of three devoted to the analysis of the regularity of solutions of elliptic problems on nonsmooth domains in ℝ3. The present paper concentrates on the regularity of solutions of the Poisson equation in neighbourhoods of edges of a polyhedral domain in the framework of the weighted Sobolev spaces and countably normed spaces. These results can be generalised to elliptic problems arising from mechanics and engineering, for instance, the elasticity problem on polyhedral domains. Hence, the results are not only important to understand comprehensively the qualitative and quantitative aspects of the behaviours of the solution and its derivatives of all orders in neighbourhoods of edges, but also essential to design an effective computation and analyse the optimal convergence of the finite elements solutions for these problems.

scholarly journals Regularity results for singular elliptic problems

2006 ◽  
Vol 4 (3) ◽  
pp. 243-259 ◽  
Author(s):  
Loredana Caso
Keyword(s):  
Boundary Conditions ◽  
Weight Function ◽  
Elliptic Equations ◽  
Global Regularity ◽  
Elliptic Problems ◽  
The Other ◽  
Weighted Spaces ◽  
Regularity Results

Some local and global regularity results for solutions of linear elliptic equations in weighted spaces are proved. Here the leading coefficients are VMO functions, while the hypotheses on the other coefficients and the boundary conditions involve a suitable weight function.

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