Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 144, pp. 1-18.

Title: Quasilinear elliptic systems in divergence form
       with weak monotonicity and nonlinear physical data

Authors: Fabien Augsburger  (Univ. of Fribourg, Switzerland)
         Norbert Hungerbuehler (Univ. of Fribourg, Switzerland)

Abstract: 
 We study the quasilinear elliptic system
 \[
 -\mathop{\rm div}\sigma(x,u,Du) =v(x)+f(x,u)+\mathop{\rm div}g(x,u)
 \]
 on a bounded domain of $\mathbb{R}^n$ with homogeneous
 Dirichlet boundary conditions.
 This system corresponds to a diffusion problem with a source $v$
 in a moving  and dissolving substance, where the motion is 
 described by $g$ and the dissolution by $f$.
 We prove existence of a weak solution of this system under
 classical regularity, growth, and coercivity conditions for 
 $\sigma$, but with only very mild monotonicity assumptions. 

Submitted August 16, 2004. Published December 7, 2004.
Math Subject Classifications: 35J60.
Key Words: Young measure; noninear elliptic systems.