2023/02/15 by Barbara Brandolini, Antoine Henrot, Brandolini, Barbara +5
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2302.07774
openalex publication_date 2023/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In tis paper we prove an isoperimetric inequality for the first twisted eigenvalue λ1,γT(Ω) of a weighted operator, defined as the minimum of the usual Rayleigh quotient when the trial functions belong to the weighted Sobolev space H01(Ω,dγ) and have weighted mean value equal to zero in Ω. We are interested in positive measures dγ=γ(x) dx for which we are able to identify the isoperimetric sets, namely, the sets that minimize λ1,γT(Ω) among sets of given weighted measure. In the cases under consideration, the optimal sets are given by two identical and disjoint copies of the isoperimetric sets (for the weighted perimeter with respect to the weighted measure).