Upper and lower bounds are determined for a function which counts the approximation numbers of the Sobolev embedding W 1,p (Ω)/ℂ → L p(Ω)/ℂ, for a wide class of domains Ω of finite volume in ℝ n and 1 < p < ∞. Results on the distribution of the eigenvalues of the Neumann Laplacian in L 2(Ω) are special consequences.
