scholarly journals Butterfly support for off diagonal coefficients and boundedness of solutions to quasilinear elliptic systems

2021 ◽  
Vol 11 (1) ◽  
pp. 672-683
Author(s):  
Salvatore Leonardi ◽  
Francesco Leonetti ◽  
Eugenio Rocha ◽  
Vasile Staicu
Keyword(s):  
Weak Solutions ◽  
Elliptic Systems ◽  
Divergence Form ◽  
Boundedness Of Solutions ◽  
Local Boundedness ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

Abstract We consider quasilinear elliptic systems in divergence form. In general, we cannot expect that weak solutions are locally bounded because of De Giorgi’s counterexample. Here we assume that off-diagonal coefficients have a “butterfly support”: this allows us to prove local boundedness of weak solutions.

Local boundedness of solutions to quasilinear elliptic systems

2011 ◽  
Vol 137 (3-4) ◽  
pp. 287-315 ◽  
Author(s):  
Giovanni Cupini ◽  
Paolo Marcellini ◽  
Elvira Mascolo
Keyword(s):  
Elliptic Systems ◽  
Boundedness Of Solutions ◽  
Local Boundedness ◽  
Quasilinear Elliptic Systems ◽  
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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