Xiaomu Ling

Solving the Dirichlet problem with prescribed density

In this paper we prove the following result. Let $\Omega\subset\mathbb R^n, n\geq 3,$ be a bounded, strictly convex, smooth domain and $\varphi: \partial\Omega\rightarrow\mathbb R$ be a smooth function. Then for any $z\in\Omega,$ there exists $c_1=c_1(\Omega, \{z\}, n, \varphi)>0,$ such that if $c\geq c_1$ then the pro...