Nonradiality of second eigenfunctions of the fractional Laplacian in a ball
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- by Jiří Benedikt, Vladimir Bobkov, Raj Narayan Dhara and Petr Girg PDF
- Proc. Amer. Math. Soc. 150 (2022), 5335-5348 Request permission
Abstract:
Using symmetrization techniques, we show that, for every $N \geq 2$, any second eigenfunction of the fractional Laplacian in the $N$-dimensional unit ball with homogeneous Dirichlet conditions is nonradial, and hence its nodal set is an equatorial section of the ball.References
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Additional Information
- Jiří Benedikt
- Affiliation: Department of Mathematics and NTIS, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 8, 301 00 Plzeň, Czech Republic
- ORCID: 0000-0001-9529-1215
- Email: benedikt@kma.zcu.cz
- Vladimir Bobkov
- Affiliation: Institute of Mathematics, Ufa Federal Research Centre, RAS, Chernyshevsky str. 112, 450008 Ufa, Russia
- MR Author ID: 1040393
- ORCID: 0000-0002-4425-0218
- Email: bobkov@matem.anrb.ru
- Raj Narayan Dhara
- Affiliation: Department of Mathematics and Statistics, Faculty of Science Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
- MR Author ID: 1085322
- ORCID: 0000-0001-6749-1500
- Email: dhara@math.muni.cz, rajnarayan.dhara@upol.cz
- Petr Girg
- Affiliation: Department of Mathematics and NTIS, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 8, 301 00 Plzeň, Czech Republic
- MR Author ID: 641198
- Email: pgirg@kma.zcu.cz
- Received by editor(s): March 16, 2021
- Received by editor(s) in revised form: February 12, 2022
- Published electronically: August 5, 2022
- Additional Notes: The second author was supported in the framework of executing the development program of Volga Region Mathematical Center (agreement no. 075-02-2022-888). The third author was supported by Mobility 3.0, Project no.: CZ.02.2.69/0.0/0.0/16_027/0008370 and Czech Science Foundation, project GJ19-14413Y
- Communicated by: Ryan Hynd
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 5335-5348
- MSC (2020): Primary 35B06, 35R11, 47A75, 35P15
- DOI: https://doi.org/10.1090/proc/16062