Abstract
We develop sharp upper bounds for energy levels of the magnetic Laplacian on starlike plane domains, under either Dirichlet or Neumann boundary conditions and assuming a constant magnetic field in the transverse direction. Our main result says that σn j=1 ψ(λjA/G) is maximal for a disk whenever ψ is concave increasing, n . 1, the domain has area A, and λj is the jth Dirichlet eigenvalue of the magnetic Laplacian iδ + B/2A(-x2, x1)2. Here the flux β is constant, and the scale invariant factor G penalizes deviations from roundness, meaning G > 1 for all domains and G = 1 for disks.
Original language | English (US) |
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Pages (from-to) | 670-689 |
Number of pages | 20 |
Journal | ESAIM - Control, Optimisation and Calculus of Variations |
Volume | 21 |
Issue number | 3 |
DOIs | |
State | Published - Jul 1 2015 |
Keywords
- Heat trace
- Isoperimetric
- Partition function
- Pauli operator
- Spectral zeta
ASJC Scopus subject areas
- Control and Systems Engineering
- Control and Optimization
- Computational Mathematics