Vol. 317, No. 2, 2022

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Isoperimetric bounds for lower-order eigenvalues

Fuquan Fang and Changyu Xia

Vol. 317 (2022), No. 2, 297–316
Abstract

New isoperimetric inequalities for lower-order eigenvalues of the Laplacian on closed hypersurfaces, of the biharmonic Steklov problems and of the Wentzell–Laplace on bounded domains in a Euclidean space are proven. Some open questions for further study are also proposed.

Keywords
isoperimetric inequalities, eigenvalues, Laplacian, biharmonic Steklov problems, Wentzell–Laplace operator
Mathematical Subject Classification
Primary: 35P15, 53C40, 53C42, 58C40
Milestones
Received: 28 October 2021
Revised: 27 January 2022
Accepted: 9 February 2022
Published: 14 July 2022
Authors
Fuquan Fang
School of Mathematics
Capital Normal University
Beijing
China
Department of Mathematics
Southern University of Science and Technology
Shenzen
Guandong
China
Changyu Xia
Department of Mathematics
Southern University of Science and Technology
Shenzen
Guandong
China