Jin Ban

Cheng--Yau logarithmic gradient estimates for positive solutions to $\Delta_f u+p\frac{|\nabla u|^2}{u}+\mu(x)u^{r}=0$ on smooth metric measure spaces

In this paper, through the combination of the Nash--Moser iteration and the Saloff-Coste-type Sobolev inequality, we establish Cheng--Yau logarithmic gradient estimates for solutions to the following nonlinear elliptic equation $$ \Delta_f u+p\frac{|\nabla u|^2}{u}+\mu(x)u^{r}=0, $$ which is closely related to the...

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