$L^{\infty }$-bounds for general singular elliptic equations with convection term

Abstract

In this note we present $L^{\infty }$-results for problems of the form $A(x,u,Du)=B(x,u,Du)$ in $\Omega$, $u>0$ in $\Omega$, $u=0$ on $\partial \Omega$, where the growth condition for the function $B:\Omega \times \mathbb{R}\times {\mathbb{R}}^N\to \mathbb{R}$ contains both a singular and a convection term. We use ideas from the works of Giacomoni-Schindler-Takac (2007) and the authors (2019) to prove the boundedness of weak solutions for such general problem by applying appropriate bootstrap arguments.