Dirichlet problem for a class of second order nonlinear elliptic systems

1990 ◽  
Vol 15 (4) ◽  
pp. 241-258 ◽  
Author(s):  
Yongzhi Xu
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Systems ◽  
Second Order ◽  
Nonlinear Elliptic Systems ◽  
Nonlinear Elliptic

scholarly journals On the regularity up to the boundary for second order nonlinear elliptic systems

1982 ◽  
Vol 99 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Mariano Giaquinta ◽  
Jindrich Necas ◽  
O. John ◽  
J. Stará
Keyword(s):  
Elliptic Systems ◽  
Second Order ◽  
Nonlinear Elliptic Systems ◽  
Nonlinear Elliptic

A pointwise differential inequality and second-order regularity for nonlinear elliptic systems

2021 ◽  
Author(s):  
Anna Kh. Balci ◽  
Andrea Cianchi ◽  
Lars Diening ◽  
Vladimir Maz’ya
Keyword(s):  
Differential Inequality ◽  
Differential Operators ◽  
Elliptic Systems ◽  
Second Order ◽  
Nonlinear Elliptic Systems ◽  
Nonlinear Elliptic ◽  
Regularity Properties ◽  
Partial Differential Operators ◽  
Global Estimates ◽  
Special Case

AbstractA sharp pointwise differential inequality for vectorial second-order partial differential operators, with Uhlenbeck structure, is offered. As a consequence, optimal second-order regularity properties of solutions to nonlinear elliptic systems in domains in $${\mathbb R^n}$$ R n are derived. Both local and global estimates are established. Minimal assumptions on the boundary of the domain are required for the latter. In the special case of the p-Laplace system, our conclusions broaden the range of the admissible values of the exponent p previously known.

POSITIVE SOLUTIONS OF NONLINEAR ELLIPTIC SYSTEMS

1993 ◽  
Vol 03 (06) ◽  
pp. 823-837 ◽  
Author(s):  
A. CAÑADA ◽  
J.L. GÁMEZ
Keyword(s):  
Positive Solutions ◽  
Nonlinear Interaction ◽  
Spatial Dependence ◽  
Global Bifurcation ◽  
Elliptic Systems ◽  
Nonlinear Elliptic Systems ◽  
Decoupling Method ◽  
Nonlinear Elliptic ◽  
Cooperative Models

In this paper we prove the existence of nonnegative and non-trivial solutions of problems of the form [Formula: see text] Our main result improves many previous results of other authors and it may be applied to study the three standard situations: competition, prey-predator and cooperative models. We also cover some other cases which, due essentially to the spatial dependence or to a nonlinear interaction, are not any of these three types. The method of proof combines a decoupling method with a global bifurcation result.

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