Asymptotic estimates of $s$-numbers of Sobolev-type embeddings

Abstract

In a quite recent paper of D. E. Edmunds and J. Lang, Asymptotic formulae for $s$-numbers of a Sobolev embedding and a Volterra type operator (published in [Rev. Mat. Complut., 29(1), 2016]) the authors obtained sharp upper and lower estimates of the approximation numbers of a Sobolev embedding involving second derivatives and of a corresponding integral operator of Volterra type. We discuss possible extensions of these results for higher order derivatives. Namely, we obtain estimates for the embedding of Sobolev type involving derivatives of order four.