Higher integrability result for nonlinear elliptic systems with conormal boundary conditions

2020 ◽  
Vol 194 ◽  
pp. 111406
Author(s):  
Youchan Kim ◽  
Seungjin Ryu ◽  
Pilsoo Shin
Keyword(s):  
Boundary Conditions ◽  
Elliptic Systems ◽  
Nonlinear Elliptic Systems ◽  
Higher Integrability ◽  
Nonlinear Elliptic

On the regularity of very weak minima

1996 ◽  
Vol 126 (2) ◽  
pp. 287-296 ◽  
Author(s):  
Daniela Giachetti ◽  
Francesco Leonetti ◽  
Rosanna Schianchi
Keyword(s):  
Weak Solutions ◽  
Elliptic Systems ◽  
Very Weak Solutions ◽  
Nonlinear Elliptic Systems ◽  
Higher Integrability ◽  
Nonlinear Elliptic ◽  
Variational Integrals ◽  
Weak Minima

We consider very weak minimisers u of variational integrals ∫ F(x, Du(x)) dx and very weak solutions u of nonlinear elliptic systems div A(x, u, Du) = 0; we prove higher integrability for the gradient Du without any homogeneity on ξ→A(x,u,ξ) thus improving on a result by Iwaniec and Sbordone.

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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