2023/12/28 by S Basak, Sagar Basak, Anisa M. H. Chorwadwala +5 · 1 citation
Computer Science · Mathematics · #35P15 #58J50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2312.16889
openalex publication_date 2023/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
We consider mixed Steklov-Dirichlet eigenvalue problem on smooth bounded domains in Riemannian manifolds. Under certain symmetry assumptions on multiconnected domains in ℝn with a spherical hole, we obtain isoperimetric inequalities for k-th Steklov-Dirichlet eigenvalues for 2 ≤ k ≤ n+1. We extend Theorem 3.1 of \citegavitone2023isoperimetric from Euclidean domains to domains in space forms, that is, we obtain sharp lower and upper bounds of the first Steklov-Dirichlet eigenvalue on bounded star-shaped domains in the unit n-sphere and in the hyperbolic space.