Electron. J. Diff. Eqns., Vol. 2004(2004), No. 144, pp. 1-18.

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

Fabien Augsburger, Norbert Hungerbühler

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.

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Fabien Augsburger
Department of Mathematics
University of Fribourg, Pérolles
1700 Fribourg, Switzerland
email: norbert.hungerbuehler@unifr.ch
Norbert Hungerbühler
Department of Mathematics
University of Fribourg, Pérolles
1700 Fribourg, Switzerland
email: norbert.hungerbuehler@unifr.ch

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