2024/05/20 by François Hamel, Emmanuel Russ, Hamel, François +1
Computer Science · Mathematics · #35P15 #47A75 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2405.12148
openalex publication_date 2024/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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^∞ constraints and minimizing or maximizing the principal eigenvalue of -Δ+v⋅∇ in a fixed domain and with a fixed parameter β>0 in the Robin condition.