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Minimizers for the fractional Sobolev inequality on domains

Frank, Rupert L. and Jin, Tianling and Xiong, Jingang (2018) Minimizers for the fractional Sobolev inequality on domains. Calculus of Variations and Partial Differential Equations, 57 (2). Art. No. 43. ISSN 0944-2669.

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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.

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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.
Funding AgencyGrant Number
Hong Kong Research Grants CouncilECS 26300716
National Natural Science Foundation of China (NSFC)11501034
National Natural Science Foundation of China (NSFC)11631002
National Natural Science Foundation of China (NSFC)11571019
Classification Code:Mathematics Subject Classification: 26D15; 31B25; 31C25; 46E35
Record Number:CaltechAUTHORS:20180221-110808137
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Official Citation:Frank, R.L., Jin, T. & Xiong, J. Calc. Var. (2018) 57: 43.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84906
Deposited By: Tony Diaz
Deposited On:21 Feb 2018 22:05
Last Modified:21 Feb 2018 22:06

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