Abdolhakim Shouman

Classification of solutions to the Liouville equation with a nonlinear Neumann boundary condition and applications to sharp inequalities

In this paper, we study the Liouville equation with a nonlinear Neumann boundary condition \begin{equation*} \begin{cases} -\Delta u = Ke^{2u}&\text{in } \mathbb{B}^{2},\\[2mm] \dfrac{\partial u}{\partial \nu}+\lambda = ke^{u}&\text{on } \partial\mathbb{B}^{2}, \end{cases} \end{equation*} where $K,k\in\mathbb{R}$, $\la...