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Eigenvalue bounds for the fractional Laplacian: A review

Frank, Rupert L. (2017) Eigenvalue bounds for the fractional Laplacian: A review. In: Recent Developments in Nonlocal Theory. De Gruyter , Berlin, pp. 210-235. ISBN 9783110571561. http://resolver.caltech.edu/CaltechAUTHORS:20170501-092157290

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Abstract

We review some recent results on eigenvalues of fractional Laplacians and fractional Schrödinger operators.We discuss, in particular, Lieb–Thirring inequalities and their generalizations, as well as semi-classical asymptotics.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1515/9783110571561-007DOIArticle
https://arxiv.org/abs/1603.09736arXivDiscussion Paper
Additional Information:© 2018 Rupert L. Frank, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 License. The author would like to thank B. Dyda, L.Geisinger, E. Lenzmann, E. Lieb, R. Seiringer and L. Silvestre for collaborations involving the fractional Laplacian. He thanks R. Bañuelos, M. Kwaśnicki, F. Maggi and R. Song for helpful comments. Partial support by U.S. National Science Foundation DMS-1363432 is acknowledged.
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Funding AgencyGrant Number
NSFDMS-1363432
Record Number:CaltechAUTHORS:20170501-092157290
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170501-092157290
Official Citation:Rupert L. Frank (2017). Eigenvalue Bounds for the Fractional Laplacian: A Review. In Giampiero Palatucci, Tuomo Kuusi (Eds.), Recent Developments in Nonlocal Theory (pp. 210–235). Warsaw, Poland: De Gruyter Open. https://doi.org/10.1515/9783110571561-007
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77096
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:01 May 2017 16:27
Last Modified:02 Aug 2018 18:10

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