Partial Regularity of Weak Solutions to the Model Venttsel Problem for Quasilinear Elliptic Systems of Equations. Method of A-Harmonic Approximation

2014 ◽  
Vol 198 (6) ◽  
pp. 655-676 ◽  
Author(s):  
A. A. Arkhipova
Keyword(s):  
Weak Solutions ◽  
Partial Regularity ◽  
Harmonic Approximation ◽  
Elliptic Systems ◽  
Systems Of Equations ◽  
Quasilinear Elliptic Systems ◽  
Regularity Of Weak Solutions ◽  
Venttsel Problem ◽  
Quasilinear Elliptic

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.

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