Jing-Bo Dou

Classification of solutions to the Liouville equation with a nonlinear Robin boundary condition on the unit disk

In this paper, we study the nonlinear boundary value problem \begin{equation*} \begin{cases} -\Delta u=e^{2u},&\mbox{in } {\mathbb{D}},\\ \frac{\partial u}{\partial\nu}+\lambda=e^u ,&\mbox{on } {\mathbb{S}^{1}}, \end{cases} \end{equation*} where $\mathbb D$ is the unit disk, $\lambda$ is a constant and $\nu$ denotes th...