Non-compact embeddings of Sobolev spaces

Summary: This study computes the precise value of the measure of noncompactness of Sobolev embeddings and proves that their noncompactness measure coincides with their norms, as well as all strict s-numbers. Furthermore, it is shown that the maximal noncompactness of Sobolev embeddings on strip-like domains remains valid even when considering Sobolev-type spaces built upon general rearrangement-invariant spaces. As a by-product, the explicit form of the first eigenfunction of the pseudo-p-Laplacian on an n-dimensional rectangle is obtained.