Entropy and approximation numbers of weighted Sobolev embeddings : a bracking technique We analyse the asymptotic behaviour of the entropy and approximation numbers of compact embeddings in limiting situations between weighted Sobolev spaces and Lebesgue spaces defined on the unit ball. The involved power weights are perturbed by slowly varying functions and have a singularity at the origin. The main results are based on a bracketing technique which extents the well known Dirichlet Neumann bracketing from spectral theory in Hilbert spaces to the general case of Banach spaces.