Published April 2018
| Submitted
Journal Article
Open
Minimizers for the fractional Sobolev inequality on domains
- Creators
-
Frank, Rupert L.
- Jin, Tianling
- Xiong, Jingang
Abstract
We consider a version of the fractional Sobolev inequality in domains and study whether the best constant in this inequality is attained. For the half-space and a large class of bounded domains we show that a minimizer exists, which is in contrast to the classical Sobolev inequalities in domains.
Additional Information
© 2018 Springer-Verlag GmbH Germany, part of Springer Nature. Received: 20 August 2017; Accepted: 25 January 2018; First Online: 17 February 2018. Part of this work was done when T. J. was visiting California Institute of Technology as an Orr foundation Caltech-HKUST Visiting Scholar during 2015-2016. He would like to thank Professor Thomas Y. Hou for hosting his visit. He also thanks Professors Zhen-Qing Chen and Dong Li for useful discussions. Partial support through National Science Foundation, grant DMS-1363432 (R.L.F.), Hong Kong RGC grant ECS 26300716 (T.J.) and NSFC 11501034, a key project of NSFC 11631002 and NSFC 11571019, (J.X.) is acknowledged.Attached Files
Submitted - 1707.00131.pdf
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Additional details
- Eprint ID
- 84906
- Resolver ID
- CaltechAUTHORS:20180221-110808137
- DMS-1363432
- NSF
- ECS 26300716
- Hong Kong Research Grants Council
- 11501034
- National Natural Science Foundation of China (NSFC)
- 11631002
- National Natural Science Foundation of China (NSFC)
- 11571019
- National Natural Science Foundation of China (NSFC)
- Created
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2018-02-21Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field