Exterior Dirichlet Problem
Exterior Dirichlet Problem
The exterior Dirichlet problem consists in finding u such that $$\displaystyle \begin {array}{rl} &Au(x)=0,\quad x\in S^-,\\ &u(x)=\mathscr {D}(x),\quad x\in {\partial S},\\ &u\in \mathscr {A}^*, \end {array} $$ where the vector function $$\mathscr {D}\in C^{(1,\alpha )}({\partial S})$$ , α ∈ (0, 1), is prescribed.