# Neumann problems for nonlinear elliptic equations with $L^1$ data

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1 Dipartimento per le Tecnologie Universita degli studi di Napoli Parthenope 2 LMRS - Laboratoire de Mathématiques Raphaël Salem 3 Dipartimento di Matematica ed Applicazioni Universita di Napoli -Federico II-

Abstract : In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is \begin{equation*} \begin{cases} -\Delta {p} u -\text{div} cx|u|^{p-2}u =f & \text{in}\ \Omega, \\ \left | abla u|^{p-2} abla u+ cx|u|^{p-2}u ight\cdot\underline n=0 & \text{on}\ \partial \Omega \,, \end{cases} \end{equation*} when $f$ is just a summable function. Our approach allows also to deduce a stability result for renormalized solutions and an existence result for operator with a zero order term.

Keywords : Nonlinear elliptic equations Neumann problems renormalized solutions existence results

Author: Maria Francesca Betta - Olivier Guibé - Anna Mercaldo -

Source: https://hal.archives-ouvertes.fr/