scholarly journals An application of a theorem of G. Zwirner to a class of non-linear elliptic systems in divergence form

2017 ◽  
Vol 11 (4) ◽  
pp. 533-539
Author(s):  
Giovanni Cimatti
Keyword(s):  
Elliptic Systems ◽  
Divergence Form ◽  
Non Linear

scholarly journals Existence and regularity results for weak solutions to (p,q)-elliptic systems in divergence form

2018 ◽  
Vol 11 (3) ◽  
pp. 273-288 ◽  
Author(s):  
Miroslav Bulíček ◽  
Giovanni Cupini ◽  
Bianca Stroffolini ◽  
Anna Verde
Keyword(s):  
Weak Solutions ◽  
Elliptic Systems ◽  
Growth Conditions ◽  
Divergence Form ◽  
Variational Structure ◽  
Non Linear ◽  
Existence And Regularity Results ◽  
Regularity Results ◽  
Higher Differentiability

AbstractWe prove existence and regularity results for weak solutions of non-linear elliptic systems with non-variational structure satisfying {(p,q)}-growth conditions. In particular, we are able to prove higher differentiability results under a dimension-free gap between p and q.

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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