L^infinity solutions for anisotropic singular elliptic equation with convection term

On Bounded Solutions for Anisotropic Singular Elliptic Equation

  • Hichem Khelifi University of Algiers 1, Algeria
  • Mokhtar Naceri ENS of Laghouat, Laghouat


In this paper we will prove the boundedness of weak solutions of nonlinear anisotropic elliptic equations of the form \begin{equation*} \begin{cases} -\sum_{i=1}^{N}D_{i}a_{i}(x,u,\nabla u))=\sum_{i=1}^{N}b_{i}(x,u,\nabla u) & \text{in } \Omega,\\ u> 0&\text{in } \Omega,\\ u= 0&\text{on } \partial\Omega,\\ \end{cases} \end{equation*} where the growth condition for the functions $b_{i} : \Omega\times\mathbb{R}\times \mathbb{R}^{N}\rightarrow\mathbb{R}$ for all $i=1,\ldots,N$ contains the singular terms and a convection term. The core concept in the proof relies on an adapted iteration technique inspired by Moser's approach. This work generalizes some results given in \cite{9}.