On the existence of extremal functions in Sobolev embedding theorems with critical exponents
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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.References
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Bibliographic Information
- A. V. Demyanov
- Affiliation: St. Petersburg State University, Russia
- Email: alex@ad9503.spb.edu
- A. I. Nazarov
- Affiliation: St. Petersburg State University, Russia
- MR Author ID: 228194
- Email: an@AN4751.spb.edu
- Received by editor(s): November 30, 2004
- Published electronically: July 20, 2006
- Additional Notes: Partially supported by the RF Ministry of Education (project no. 4733), and by RFBR (grant no. 05–01–01063).
- © Copyright 2006 American Mathematical Society
- Journal: St. Petersburg Math. J. 17 (2006), 773-796
- MSC (2000): Primary 49J10, 35J20, 35J60
- DOI: https://doi.org/10.1090/S1061-0022-06-00929-0
- MathSciNet review: 2241425
Dedicated: In memory of Ol $\cprime$ga Aleksandrovna Ladyzhenskaya