Journal
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
Volume 21, Issue 3, Pages 670-689Publisher
EDP SCIENCES S A
DOI: 10.1051/cocv/2014043
Keywords
Isoperimetric; spectral zeta; heat trace; partition function; Pauli operator
Categories
Funding
- Simons Foundation [204296]
- National Science Foundation [DMS-0803120]
- Polish National Science Centre (NCN) [2012/07/B/ST1/03356]
- Banff International Research Station
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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 Sigma(n)(j=1) Phi(lambda(j) A/G) is maximal for a disk whenever F is concave increasing, n >= 1, the domain has area A, and lambda(j) is the jth Dirichlet eigenvalue of the magnetic Laplacian (i del + beta/2A(-x(2),x(1)))(2). Here the flux beta is constant, and the scale invariant factor G penalizes deviations from roundness, meaning G >= 1 for all domains and G = 1 for disks.
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