Universal constraints on the location of extrema of eigenfunctions of non-local Schrödinger operators
journal contributionposted on 2017-11-29, 15:31 authored 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.
This research of AB was supported in part by an INSPIRE faculty fellowship and a DST-SERB grant EMR/2016/004810.
- Mathematical Sciences
Published inJournal of Differential Equations
Pages267 - 306
CitationBISWAS, 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.
- AM (Accepted Manuscript)
Publisher statementThis 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.