On Uniqueness of a Solution of $Lu=u^\alpha$ with Given Trace
On Uniqueness of a Solution of $Lu=u^\alpha$ with Given Trace
A boundary trace $(\Gamma, \nu)$ of a solution of $\Delta u = u^\alpha$ in a bounded smooth domain in $\mathbb{R}^d$ was first constructed by Le Gall who described all possible traces for $\alpha = 2, d= 2$ in which case a solution is defined uniquely by its trace. In a …