Estimates for solutions to nonlinear degenerate elliptic equations with lower order terms

2019 ◽  
Vol 69 (1) ◽  
pp. 367-384
Author(s):  
Maria Francesca Betta ◽  
Adele Ferone ◽  
Gabriella Paderni
Keyword(s):  
Lower Order ◽  
Elliptic Equations ◽  
Degenerate Elliptic Equations ◽  
Degenerate Elliptic ◽  
Lower Order Terms ◽  
Nonlinear Degenerate

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.

scholarly journals Generalized Keller-Osserman Conditions for Fully Nonlinear Degenerate Elliptic Equations

2018 ◽  
Vol 64 (1) ◽  
pp. 74-85
Author(s):  
I Capuzzo Dolcetta ◽  
F Leoni ◽  
A Vitolo
Keyword(s):  
Elliptic Equations ◽  
A Priori ◽  
Sufficient Conditions ◽  
Degenerate Elliptic Equations ◽  
Fully Nonlinear ◽  
Degenerate Elliptic ◽  
Whole Space ◽  
Necessary And Sufficient ◽  
Lower Order Terms ◽  
Nonlinear Degenerate

We discuss the existence of entire (i.e. defined on the whole space) subsolutions of fully nonlinear degenerate elliptic equations, giving necessary and sufficient conditions on the coefficients of the lower order terms which extend the classical Keller-Osserman conditions for semilinear elliptic equations. Our analysis shows that, when the conditions of existence of entire subsolutions fail, a priori upper bounds for local subsolutions can be obtained.

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.

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