scholarly journals Weak solution for nonlinear degenerate elliptic problem with Dirichlet-type boundary condition in weighted Sobolev spaces

2021 ◽  
pp. 1-17
Author(s):  
Abdelali Sabri ◽  
Ahmed Jamea ◽  
Hamad Talibi Alaoui
Keyword(s):  
Boundary Condition ◽  
Weak Solution ◽  
Sobolev Spaces ◽  
Elliptic Problem ◽  
Weighted Sobolev Spaces ◽  
Dirichlet Type ◽  
Degenerate Elliptic ◽  
Type Boundary ◽  
Type Boundary Condition ◽  
Nonlinear Degenerate

scholarly journals Neumann and Robin type boundary conditions in Fractional Orlicz-Sobolev spaces

2020 ◽  
Author(s):  
Sabri Bahrouni ◽  
Ariel Salort
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Nonlocal Problem ◽  
Nonlocal Problems ◽  
Different Boundary Conditions ◽  
Nonstandard Growth ◽  
Type Boundary ◽  
Type Boundary Condition

In the first part of this article we deal with the existence of at least three non-trivial weak solutions of a nonlocal problem with nonstandard growth involving a nonlocal Robin type boundary condition. The second part of the article is devoted to study eigenvalues and minimizers of  several nonlocal problems for the fractional $g-$Laplacian $(-\Delta_g)^s$ with different boundary conditions, namely, Dirichlet, Neumann and Robin.

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 -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 .

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