Existence of bounded solutions to some nonlinear degenerate elliptic systems

Pages: 191 - 203, Volume 11, Issue 1, January 2009

doi:10.3934/dcdsb.2009.11.191       Abstract        Full Text (185.3K)       Related Articles

Francesco Leonetti - Università di L'Aquila, Dipartimento di Matematica Pura ed Applicata, Via Vetoio, Coppito, 67100 L'Aquila, Italy (email)
Pier Vincenzo Petricca - Via Sant’Amasio 18, 03039 Sora, Italy (email)

Abstract: We prove existence of bounded weak solutions $u: \Omega \subset \R^{n} \to \R^{N}$ for the Dirichlet problem

-div $( a(x, u(x), Du(x) ) ) = f(x),$ $ x \in \Omega$;
$u(x) = 0, $ $ x \in \partial\Omega$

where $\Omega$ is a bounded open set, $a$ is a suitable degenerate elliptic operator and $f$ has enough integrability.

Keywords:  Existence, bounded, solution, nonlinear, elliptic, system, degenerate, coercivit
Mathematics Subject Classification:  Primary: 35J55, 35J60; Secondary: 35J7

Received: November 2007;      Revised: June 2008;      Published: November 2008.