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.