Existence Result for a Second Order Nonlinear Degenerate Elliptic Equation in Weighted Orlicz-Sobolev Spaces

2002 ◽  
Author(s):  
M Arias ◽  
E Azroul
Keyword(s):  
Elliptic Equation ◽  
Sobolev Spaces ◽  
Existence Result ◽  
Degenerate Elliptic Equation ◽  
Second Order ◽  
Degenerate Elliptic ◽  
Nonlinear Degenerate

scholarly journals An oscillation theorem for the nonlinear degenerate elliptic equation in the Heisenberg group

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Duan Wu ◽  
Pengcheng Niu
Keyword(s):  
Elliptic Equation ◽  
Heisenberg Group ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Degenerate Elliptic Equation ◽  
Oscillation Theorem ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
Oscillation Of Solutions ◽  
Nonlinear Degenerate

AbstractThe aim of this paper is to study the oscillation of solutions of the nonlinear degenerate elliptic equation in the Heisenberg group $H^{n}$ H n . We first derive a critical inequality in $H^{n}$ H n . Based on it, we establish a Picone-type differential inequality and a Sturm-type comparison principle. Then we obtain an oscillation theorem. Our result generalizes the related conclusions for the nonlinear elliptic equations in $R^{n}$ R n .

scholarly journals Solvability of nonlinear Dirichlet problem for a class of degenerate elliptic equations

2004 ◽  
Vol 2004 (3) ◽  
pp. 205-214
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Existence Result ◽  
Differential Operators ◽  
Degenerate Elliptic Equation ◽  
Degenerate Elliptic Equations ◽  
Nonlinear Dirichlet Problem ◽  
Partial Differential Operators ◽  
Degenerate Elliptic ◽  
Nonlinear Degenerate

We prove an existence result for solution to a class of nonlinear degenerate elliptic equation associated with a class of partial differential operators of the formLu(x)=∑i,j=1nDj(aij(x)Diu(x)), withDj=∂/∂xj, whereaij:Ω→ℝare functionssatisfying suitable hypotheses.

scholarly journals On a regularity of biharmonic approximations to a nonlinear degenerate elliptic PDE

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1835-1842
Author(s):  
Andrej Novak ◽  
Jela Susic
Keyword(s):  
Elliptic Equation ◽  
Degenerate Elliptic Equation ◽  
Chebyshev Inequality ◽  
Elliptic Pde ◽  
Numerical Example ◽  
Degenerate Elliptic ◽  
Rough Coefficients ◽  
Approximation Parameter ◽  
Nonlinear Degenerate

Under appropriate assumption on the coefficients, we prove that a sequence of biharmonic regularization to a nonlinear degenerate elliptic equation with possibly rough coefficients preserves certain regularity as the approximation parameter tends to zero. In order to obtain the result, we introduce a generalization of the Chebyshev inequality. We also present numerical example.

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.

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