Hadamard’s Variational Formula for Simple Eigenvalues
Here, we study Hadamard’s variational formula for simple eigenvalues under dynamical and conformal deformations. Particularly, harmonic convexity of the first eigenvalue of the Laplacian under the mixed boundary condition is established for a two-dimensional domain, which implies several new inequal...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-10-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/4/4/65 |
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| author | Takashi Suzuki Takuya Tsuchiya |
| author_facet | Takashi Suzuki Takuya Tsuchiya |
| author_sort | Takashi Suzuki |
| collection | DOAJ |
| description | Here, we study Hadamard’s variational formula for simple eigenvalues under dynamical and conformal deformations. Particularly, harmonic convexity of the first eigenvalue of the Laplacian under the mixed boundary condition is established for a two-dimensional domain, which implies several new inequalities. |
| format | Article |
| id | doaj-art-80ffee644e9c4e989fb32d3f930bf284 |
| institution | DOAJ |
| issn | 2673-9909 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj-art-80ffee644e9c4e989fb32d3f930bf2842025-08-20T02:55:31ZengMDPI AGAppliedMath2673-99092024-10-01441211122910.3390/appliedmath4040065Hadamard’s Variational Formula for Simple EigenvaluesTakashi Suzuki0Takuya Tsuchiya1Center for Mathematical Modeling and Data Science, Osaka University, Osaka 565-0871, JapanCenter for Mathematical Modeling and Data Science, Osaka University, Osaka 565-0871, JapanHere, we study Hadamard’s variational formula for simple eigenvalues under dynamical and conformal deformations. Particularly, harmonic convexity of the first eigenvalue of the Laplacian under the mixed boundary condition is established for a two-dimensional domain, which implies several new inequalities.https://www.mdpi.com/2673-9909/4/4/65eigenvalue problemperturbation theory of linear operatorsdomain deformationHadamard’s variational formulaGarabadian–Schiffer’s formula |
| spellingShingle | Takashi Suzuki Takuya Tsuchiya Hadamard’s Variational Formula for Simple Eigenvalues AppliedMath eigenvalue problem perturbation theory of linear operators domain deformation Hadamard’s variational formula Garabadian–Schiffer’s formula |
| title | Hadamard’s Variational Formula for Simple Eigenvalues |
| title_full | Hadamard’s Variational Formula for Simple Eigenvalues |
| title_fullStr | Hadamard’s Variational Formula for Simple Eigenvalues |
| title_full_unstemmed | Hadamard’s Variational Formula for Simple Eigenvalues |
| title_short | Hadamard’s Variational Formula for Simple Eigenvalues |
| title_sort | hadamard s variational formula for simple eigenvalues |
| topic | eigenvalue problem perturbation theory of linear operators domain deformation Hadamard’s variational formula Garabadian–Schiffer’s formula |
| url | https://www.mdpi.com/2673-9909/4/4/65 |
| work_keys_str_mv | AT takashisuzuki hadamardsvariationalformulaforsimpleeigenvalues AT takuyatsuchiya hadamardsvariationalformulaforsimpleeigenvalues |