Electronic Journal of Differential Equations,
Conference 09 (2002), pp. 183-202. 

Title: Nonlinear equations with natural growth terms and measure data.   

Authors: Alessio  Porretta (Univ. di Roma, Tor Vergata, Roma, Italia)   
 
Abstract: 
  We consider  a class of nonlinear elliptic equations containing
  a $p$-Laplacian type operator, lower order terms having natural 
  growth with respect to the gradient, and bounded measures as data. 
  The model example is the equation
  $$ -\Delta_p(u) + g(u)|\nabla u|^p=\mu  
  $$ 
  in a bounded set $\Omega\subset \mathbb{R}^N$, coupled with a  
  Dirichlet boundary condition. We provide a  review of the 
  results recently obtained in the absorption case (when $g(s)s\geq0$)
  and prove  a new  existence result  without any sign condition on $g$, 
  assuming only that $g\in L^1({\bf R})$. This latter assumption is 
  proved to be optimal for existence of solutions for any measure $\mu$.

Published December 28, 2002.
Math Subject Classifications: 35J60, 35J65, 35R05.   
Key Words: Nonlinear elliptic equations; natural growth terms; measure data.