The monotonicity condition and a priori estimates of the Hölder norm for a class of nondiagonal elliptic systems with quadratic nonlinearity

2007 ◽  
Vol 142 (1) ◽  
pp. 1733-1748
Author(s):  
A. A. Arkhipova
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Systems ◽  
Quadratic Nonlinearity ◽  
Monotonicity Condition ◽  
Hölder Norm ◽  
Priori Estimates

scholarly journals Quasilinear elliptic systems in divergence form associated to general nonlinearities

2018 ◽  
Vol 7 (4) ◽  
pp. 425-447 ◽  
Author(s):  
Lorenzo D’Ambrosio ◽  
Enzo Mitidieri
Keyword(s):  
Positive Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Systems ◽  
Divergence Form ◽  
Systems Of Equations ◽  
Quasilinear Elliptic Systems ◽  
Open Set ◽  
Priori Estimates ◽  
Quasilinear Elliptic

AbstractThe paper is concerned with a priori estimates of positive solutions of quasilinear elliptic systems of equations or inequalities in an open set of {\Omega\subset\mathbb{R}^{N}} associated to general continuous nonlinearities satisfying a local assumption near zero. As a consequence, in the case {\Omega=\mathbb{R}^{N}}, we obtain nonexistence theorems of positive solutions. No hypotheses on the solutions at infinity are assumed.

scholarly journals Singular quasilinear convective elliptic systems in ℝ N

2022 ◽  
Vol 11 (1) ◽  
pp. 741-756
Author(s):  
Umberto Guarnotta ◽  
Salvatore Angelo Marano ◽  
Abdelkrim Moussaoui
Keyword(s):  
Fixed Point ◽  
Weak Solution ◽  
Elliptic System ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Systems ◽  
Perturbation Techniques ◽  
Priori Estimates ◽  
Regularity Results

Abstract The existence of a positive entire weak solution to a singular quasi-linear elliptic system with convection terms is established, chiefly through perturbation techniques, fixed point arguments, and a priori estimates. Some regularity results are then employed to show that the obtained solution is actually strong.

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