scholarly journals Weighted Sobolev Spaces and Degenerate Elliptic Equations

2008 ◽  
Vol 26 (1-2) ◽  
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Weighted Sobolev Spaces ◽  
Degenerate Elliptic Equations ◽  
Degenerate Elliptic

scholarly journals -Solutions for Some Nonlinear Degenerate Elliptic Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Dirichlet Problem ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Weighted Sobolev Spaces ◽  
Quasilinear Elliptic Equations ◽  
Degenerate Elliptic Equations ◽  
Degenerate Elliptic ◽  
Quasilinear Elliptic ◽  
Nonlinear Degenerate

We are interested in the existence of solutions for Dirichlet problem associated to the degenerate quasilinear elliptic equations in the setting of the weighted Sobolev spaces .

scholarly journals Existence Results For A Class Of Nonlinear Degenerate Elliptic Equations

2019 ◽  
Vol 5 (2) ◽  
pp. 164-178
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Weighted Sobolev Spaces ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Degenerate Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
Nonlinear Degenerate

AbstractIn this paper we are interested in the existence of solutions for Dirichlet problem associated with the degenerate nonlinear elliptic equations\left\{ {\matrix{ { - {\rm{div}}\left[ {\mathcal{A}\left( {x,\nabla u} \right){\omega _1} + \mathcal{B}\left( {x,u,\nabla u} \right){\omega _2}} \right] = {f_0}\left( x \right) - \sum\limits_{j = 1}^n {{D_j}{f_j}\left( x \right)\,\,{\rm{in}}} \,\,\,\,\,\Omega ,} \hfill \cr {u\left( x \right) = 0\,\,\,\,{\rm{on}}\,\,\,\,\partial \Omega {\rm{,}}} \hfill \cr } } \right.in the setting of the weighted Sobolev spaces.

Existence Theorems for a Class of Edge-Degenerate Elliptic Equations on Singular Manifolds

2015 ◽  
Vol 58 (2) ◽  
pp. 355-377
Author(s):  
Haining Fan
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Mountain Pass Theorem ◽  
Existence Theorems ◽  
Nehari Manifold ◽  
Mountain Pass ◽  
Degenerate Elliptic Equations ◽  
Degenerate Elliptic ◽  
The Nehari Manifold ◽  
Singular Manifolds

AbstractIn this paper we establish the Nehari manifold on edge Sobolev spaces and study some of their properties. Furthermore, we use these results and the mountain pass theorem to get non-negative solutions of a class of edge-degenerate elliptic equations on singular manifolds under different conditions.

scholarly journals Existence and uniqueness of solution for a class of nonlinear degenerate elliptic equation in weighted Sobolev spaces

2017 ◽  
Vol 9 (1) ◽  
pp. 26-44
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Spaces ◽  
Nonlinear Elliptic Equations ◽  
Degenerate Elliptic Equation ◽  
Uniqueness Of Solutions ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
Nonlinear Degenerate

AbstractIn this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations$$\matrix{{\Delta {\rm{(v}}({\rm{x}})\left| {\Delta {\rm{u}}} \right|^{{\rm{r}} - 2} \Delta {\rm{u}}) - \sum\limits_{{\rm{j}} = 1}^{\rm{n}} {{\rm{D}}_{\rm{j}} [{\rm{w}}_1 ({\rm{x}}){\cal{A}}_{\rm{j}} ({\rm{x}},{\rm{u}},\nabla {\rm{u}})]} } \hfill \cr { + \;{\rm{b}}({\rm{x}},{\rm{u}},\nabla {\rm{u}})\;{\rm{w}}_2 ({\rm{x}}) = {\rm{f}}_0 ({\rm{x}}) - \sum\limits_{{\rm{j}} = 1}^{\rm{n}} {{\rm{D}}_{\rm{j}} {\rm{f}}_{\rm{j}} ({\rm{x}}),\;\;\;\;\;{\rm{in}}\;\Omega } }}$$in the setting of the Weighted Sobolev Spaces.

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.

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