2020/01/08 by Pavel Exner, Exner, Pavel, Vladimir Lotoreichik +1
Computer Science · Mathematics · #35J05 #35P20 #47A75 #49R05 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Quantum Physics (quant-ph) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2001.02718
openalex publication_date 2020/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper we deal with spectral optimization for the Robin Laplacian on a family of planar domains admitting parallel coordinates, namely a fixed-width strip built over a smooth closed curve and the exterior of a convex set with a smooth boundary. We show that if the curve length is kept fixed, the first eigenvalue referring to the fixed-width strip is for any value of the Robin parameter maximized by a circular annulus. Furthermore, we prove that the second eigenvalue in the exterior of a convex domain Ω corresponding to a negative Robin parameter does not exceed the analogous quantity for a disk whose boundary has a curvature larger than or equal to the maximum of that for ∂Ω.