A Faber-Krahn inequality for the Laplacian with drift under Robin boundary condition
- Resource Type
- Working Paper
- Authors
- Hamel, François; Russ, Emmanuel
- Source
- Subject
- Mathematics - Analysis of PDEs
35P15, 47A75
- Language
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.
Comment: 16 pages