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