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For limiting non-compact Sobolev embeddings into continuous functions westudy behavior of Approximation, Gelfand, Kolmogorov, Bernstein and Isomorphisms-numbers. In the one dimensional case the exact values of the above-mentionedstrict s-numbers were obtained and in the higher dimensions sharp estimates forasymptotic behavior of strict s-numbers were established. As all known resultsfor s-numbers of Sobolev type embeddings are studied mainly under thecompactness assumption then our work is an extension of existing results andreveal an interesting behavior of s-numbers in the limiting case when some ofthem (Approximation, Gelfand and Kolmogorov) have positive lower bound andothers (Bernstein and Isomorphism) are decreasing to zero. From our resultsalso follows that such limiting non-compact Sobolev embeddings are finitelystrictly singular maps.

Strict s-numbers of non-compact Sobolev embeddings into continuous functions