On the existence of extremal functions in Sobolev embedding theorems with critical exponents

Demyanov, A.; Nazarov, A.

doi:10.1090/S1061-0022-06-00929-0

On the existence of extremal functions in Sobolev embedding theorems with critical exponents
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by A. V. Demyanov and A. I. Nazarov
Translated by: A. I. Nazarov

St. Petersburg Math. J. 17 (2006), 773-796

DOI: https://doi.org/10.1090/S1061-0022-06-00929-0

Published electronically: July 20, 2006

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Abstract:

Sufficient conditions for the existence of extremal functions in Sobolev-type inequalities on manifolds with or without boundary are established. Some of these conditions are shown to be sharp. Similar results for embeddings in some weighted $L_q$-spaces are obtained.

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