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Universal constraints on the location of extrema of eigenfunctions of non-local Schrödinger operators

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journal contribution
posted on 29.11.2017, 15:31 by Anup Biswas, Jozsef Lorinczi
We derive a lower bound on the location of global extrema of eigenfunctions for a large class of non-local Schrödinger operators in convex domains under Dirichlet exterior conditions, featuring the symbol of the kinetic term, the strength of the potential, and the corresponding eigenvalue, and involving a new universal constant. We show a number of probabilistic and spectral geometric implications, and derive a Faber-Krahn type inequality for non-local operators. Our study also extends to potentials with compact support, and we establish bounds on the location of extrema relative to the boundary edge of the support or level sets around minima of the potential.

Funding

This research of AB was supported in part by an INSPIRE faculty fellowship and a DST-SERB grant EMR/2016/004810.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Differential Equations

Volume

267

Issue

1

Pages

267 - 306

Citation

BISWAS, A. and LORINCZI, J., 2019. Universal constraints on the location of extrema of eigenfunctions of non-local Schrödinger operators. Journal of Differential Equations, 267 (1), pp.267-306.

Publisher

© Elsevier

Version

AM (Accepted Manuscript)

Publisher statement

This paper was accepted for publication in the journal Journal of Differential Equations and the definitive published version is available at https://doi.org/10.1016/j.jde.2019.01.007.

Publication date

2019-01-17

ISSN

0022-0396

Language

en