Spectral optimization problems for potentials and measures

2013/10/06 by Dorin Bucur, Bucur, Dorin, Giuseppe Buttazzo +3
Computer Science · Mathematics · #49J45 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Spectral Theory in Mathematical Physics #math.AP #math.OC #msc:49J45

paper · pdf · doi:10.48550/arxiv.1310.1568

30 pages, 1 figure

arxiv created 2013/10/06 · openalex publication_date 2013/10/06 · arxiv updated 2013/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper we consider spectral optimization problems involving the Schrödinger operator -Δ+μ on \R^d, the prototype being the minimization of the k the eigenvalue λ_k(μ). Here μ may be a capacitary measure with prescribed torsional rigidity (like in the Kohler-Jobin problem) or a classical nonnegative potential V which satisfies the integral constraint \ds ∫ V^-pdx ≤ m with 0<p<1. We prove the existence of global solutions in \R^d and that the optimal potentials or measures are equal to +∞ outside a compact set.

Related

• Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity
• Optimal Potentials For Schrodinger Operators
• Some New Problems in Spectral Optimization
• Conditions of discreteness of the spectrum for Schr "odinger operator\n and some optimization problems for capacity and measures
• Optimal design problems for Schrödinger operators with noncompact resolvents