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arXiv · 2405.12148

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

François Hamel·Emmanuel Russ
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Abstract

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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François Hamel, Emmanuel Russ. 2024-05-20. A Faber-Krahn inequality for the Laplacian with drift under Robin boundary condition. https://arxiv.org/abs/2405.12148

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