A Faber-Krahn inequality for the Laplacian with drift under Robin boundary condition - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

A Faber-Krahn inequality for the Laplacian with drift under Robin boundary condition

Résumé

We prove a Faber-Krahn inequality for the Laplacian with drift under Robin boundary condition, provided that the $\beta$ 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 $\beta$ 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 $-\Delta+v\cdot\nabla$ in a fixed domain and with a fixed parameter $\beta>0$ in the Robin condition.
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Dates et versions

hal-04532775 , version 1 (04-04-2024)
hal-04532775 , version 2 (27-09-2024)

Identifiants

  • HAL Id : hal-04532775 , version 1

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François Hamel, Emmanuel Russ. A Faber-Krahn inequality for the Laplacian with drift under Robin boundary condition. 2024. ⟨hal-04532775v1⟩
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