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.