Gradient estimates for nonlinear elliptic equations with a gradient-dependent nonlinearity

17 Jul 2018 Ching Joshua Cirstea Florica C.

In this paper, we obtain gradient estimates of the positive solutions to weighted $p$-Laplacian type equations with a gradient-dependent nonlinearity of the form \begin{equation} \label{one} {\rm div} (|x|^{\sigma}|\nabla u|^{p-2} \nabla u)= |x|^{-\tau} u^q |\nabla u|^m \quad \mbox{in } \ \Omega^*:= \Omega \setminus \{ 0 \}. \end{equation} Here, $\Omega\subseteq \mathbb R^N$ denotes a domain containing the origin with $N\geq 2$, whereas $m,q\in [0,\infty)$, $1<p\leq N+\sigma$ and $q>\max\{p-m-1,\sigma+\tau-1\}$... (read more)

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