Mathematics – Analysis of PDEs
Scientific paper
2011-04-07
Mathematics
Analysis of PDEs
19 pages, 1 figure
Scientific paper
The sum of the first n energy levels of the planar Laplacian with constant magnetic field of given total flux is shown to be maximal among triangles for the equilateral triangle, under normalization of the ratio (moment of inertia)/(area)^3 on the domain. The result holds for both Dirichlet and Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary conditions too. The square similarly maximizes the eigenvalue sum among parallelograms, and the disk maximizes among ellipses. More generally, a domain with rotational symmetry will maximize the magnetic eigenvalue sum among all linear images of that domain. These results are new even for the ground state energy (n=1).
Laugesen Richard S.
Liang Jian-Jie
Roy Arindam
No associations
LandOfFree
Sums of magnetic eigenvalues are maximal on rotationally symmetric domains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Sums of magnetic eigenvalues are maximal on rotationally symmetric domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sums of magnetic eigenvalues are maximal on rotationally symmetric domains will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-717843