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On the second eigenvalue of combination between local and nonlocal $ p$-Laplacian


Authors: Divya Goel and K. Sreenadh
Journal: Proc. Amer. Math. Soc. 147 (2019), 4315-4327
MSC (2010): Primary 35P30, 49Q10; Secondary 47J10
DOI: https://doi.org/10.1090/proc/14542
Published electronically: June 27, 2019
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Abstract: In this paper, we study the mountain pass characterization of the second eigenvalue of the operator $ -\Delta _p u -\Delta _{J,p}u$ and study shape optimization problems related to these eigenvalues.


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Additional Information

Divya Goel
Affiliation: Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khaz, New Delhi-110016, India
Email: divyagoel2511@gmail.com

K. Sreenadh
Affiliation: Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khaz, New Delhi-110016, India
Email: sreenadh@maths.iitd.ac.in

DOI: https://doi.org/10.1090/proc/14542
Keywords: Nonlocal $p$-Laplacian, eigenvalue problem, Faber-Krahn inequality, nonlocal Hong-Krahn-Szeg\H{o} inequality.
Received by editor(s): August 30, 2018
Received by editor(s) in revised form: January 7, 2019
Published electronically: June 27, 2019
Communicated by: Catherine Sulem
Article copyright: © Copyright 2019 American Mathematical Society