RMC - Vol 2 Num 2, 3 - J.-P. Raimond

Full paper in PDF:
$% J.-P. Raimond, Régularité globale des solutions de systèmes elliptiques non linéaires, Rev. Mat. Complut. 2 (1989), no. 2, 3, 242–270.%$

Régularité globale des solutions de systèmes elliptiques non linéaires

Jean-Pierre RAIMOND

Laboratoire d’Analyse Numérique
Université Paul Sabatier
118, Route de Narbonne
31062 Toulouse Cedex — France

Received: December 12, 1988

ABSTRACT

We consider the regularity of functions $u (- W 1,p(_O_,Rm) 0$ solving elliptic degenerated or singular systems of the type:

- -@-(aai (x, \~/ u(x)))= fi(x,u(x)). @xn

We suppose that $a ai (x,v)$ satisfies a growth condition of order $(p- 1)$ with respect to $v$ .

We show that, if $p< 2$ , the solutions of the system belong to $2,np/(n+p-2) W$ , if $p> 2$ and $n >2$ , they belong to $1,np/(n- 2) W$ and if $p> 2$ and $n =2$ , they belong to $1,r W$ for every $r < +o o$ .

2000 Mathematics Subject Classification: 35J70, 35B65.