BOUNDARY REGULARITY FOR QUASILINEAR ELLIPTIC SYSTEMS

2002 ◽  
Vol 27 (11-12) ◽  
pp. 2491-2512 ◽  
Author(s):  
Joseph F. Grotowski
Keyword(s):  
Elliptic Systems ◽  
Boundary Regularity ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

scholarly journals Regularity Result for Quasilinear Elliptic Systems with Super Quadratic Natural Growth Condition

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Shuhong Chen ◽  
Zhong Tan
Keyword(s):  
Growth Condition ◽  
Elliptic Systems ◽  
Regularity Result ◽  
Boundary Regularity ◽  
Quadratic Growth ◽  
Natural Growth ◽  
General Criterion ◽  
Natural Growth Condition ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

We consider boundary regularity for weak solutions of second-order quasilinear elliptic systems under natural growth condition with super quadratic growth and obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. Combined with existing results on interior partial regularity, this result yields an upper bound on the Hausdorff dimension of the singular set at the boundary.

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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