Journal
DUKE MATHEMATICAL JOURNAL
Volume 171, Issue 12, Pages 2407-2459Publisher
DUKE UNIV PRESS
DOI: 10.1215/00127094-2022-0051
Keywords
Appendix B; Spectral analysis 2451; [2]; [3]; [6]; [8]-[10]; [25]; [26]; [29]; [31]; [35]-[37]); isoperimetric inequalities (see
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Funding
- European Research Council [721675]
- European Research Council (ERC) [721675] Funding Source: European Research Council (ERC)
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This article proves a sharp quantitative version of the p-Sobolev inequality, with a control on the maximum possible distance from the class of optimal functions. Surprisingly, the sharp exponent is constant for p < 2, while it depends on p for p > 2.
We prove a sharp quantitative version of the p-Sobolev inequality for any 1 < p < n, with a control on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent is constant for p < 2, while it depends on p for p > 2.
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