Published May 2, 2017
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Remainder terms in the fractional Sobolev inequality
- Creators
- Chen, Shibing
- Frank, Rupert L.
- Weth, Tobias
Abstract
We show that the fractional Sobolev inequality for the embedding H^(s/2)(R^N),↪ L^(2N)/_(N-s) (R^N) s ∈ (0,N) can be sharpened by adding a remainder term proportional to the distance to the set of optimizers. As a corollary, we derive the existence of a remainder term in the weak L^N/_(N−s)-norm for functions supported in a domain of finite measure. Our results generalize earlier work for the non-fractional case where s is an even integer.
Additional Information
(Submitted on 25 May 2012) U.S. National Science Foundation grant PHY-1068285 (R.F.) and German Science Foundation (DFG) grant WE 2821/4-1 (T.W.) is acknowledged. Shibing Chen wants to thank Robert McCann for helpful discussions.Attached Files
Submitted - 1205.5666.pdf
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Additional details
- Eprint ID
- 77132
- Resolver ID
- CaltechAUTHORS:20170502-150250004
- PHY-1068285
- NSF
- WE 2821/4-1
- Deutsche Forschungsgemeinschaft (DFG)
- Created
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2017-05-02Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field