A Faber-Krahn inequality for the Laplacian with drift under Robin boundary condition
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910453157855232 |
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| author | Hamel, François Russ, Emmanuel |
| author_facet | Hamel, François Russ, Emmanuel |
| contents | We prove a Faber-Krahn inequality for the Laplacian with drift under Robin boundary condition, provided that the $β$ parameter in the Robin condition is large enough. The proof relies on a compactness argument, on the convergence of Robin eigenvalues to Dirichlet eigenvalues when $β$ goes to infinity, and on a strict Faber-Krahn inequality under Dirichlet boundary condition. We also show the existence and uniqueness of drifts $v$ satisfying some $L^\infty$ constraints and minimizing or maximizing the principal eigenvalue of $-Δ+v\cdot\nabla$ in a fixed domain and with a fixed parameter $β>0$ in the Robin condition. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_12148 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Faber-Krahn inequality for the Laplacian with drift under Robin boundary condition Hamel, François Russ, Emmanuel Analysis of PDEs 35P15, 47A75 We prove a Faber-Krahn inequality for the Laplacian with drift under Robin boundary condition, provided that the $β$ parameter in the Robin condition is large enough. The proof relies on a compactness argument, on the convergence of Robin eigenvalues to Dirichlet eigenvalues when $β$ goes to infinity, and on a strict Faber-Krahn inequality under Dirichlet boundary condition. We also show the existence and uniqueness of drifts $v$ satisfying some $L^\infty$ constraints and minimizing or maximizing the principal eigenvalue of $-Δ+v\cdot\nabla$ in a fixed domain and with a fixed parameter $β>0$ in the Robin condition. |
| title | A Faber-Krahn inequality for the Laplacian with drift under Robin boundary condition |
| topic | Analysis of PDEs 35P15, 47A75 |
| url | https://arxiv.org/abs/2405.12148 |