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Multiplicities
of eigenvalues for the Laplace operator on a square
Siqi Fu, Jack Heimrath and Samuel Hsiao |
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Vol. 18 (2025), No. 3, 487–494
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Abstract |
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We establish a formula for multiplicities of eigenvalues for the Laplace operator subject to the Dirichlet boundary condition on a square. In particular, we show that, for any given positive integer , there is an eigenvalue whose multiplicity is exactly . |
Keywords
Laplace operator, eigenvalue, multiplicity, Legendre's
formula
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Mathematical Subject Classification
Primary: 35P15
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Milestones
Received: 18 August 2023
Revised: 18 September 2023
Accepted: 18 September 2023
Published: 28 April 2025
Communicated by Martin Bohner
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Authors |
| Siqi Fu | |
| Department of Mathematical
Sciences Rutgers University-Camden Camden, NJ United States |
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| Jack Heimrath | |
| Department of Mathematics and
Statistics Queen’s University Kingston, ON Canada |
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| Samuel Hsiao | |
| Department of Chemistry Rutgers University-Camden Camden, NJ United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
