539 citations · 6.8k across the 160 of their papers we have counts for
5 papers · 1 filter
Equivalence of Sobolev inequalities and Lieb-Thirring inequalities
Rupert L. Frank, Elliott H. Lieb, Robert Seiringer
We show that, under very general definitions of a kinetic energy operator , the Lieb-Thirring inequalities for sums of eigenvalues of can be derived from the Sobolev inequ…
Modulated phases of a 1D sharp interface model in a magnetic field
Alessandro Giuliani, Joel L. Lebowitz, Elliott H. Lieb
We investigate the ground states of 1D continuum models having short-range ferromagnetic type interactions and a wide class of competing longer-range antiferromagnetic type interac…
Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality
Rupert L. Frank, Elliott H. Lieb
We give a new proof of certain cases of the sharp HLS inequality. Instead of symmetric decreasing rearrangement it uses the reflection positivity of inversions in spheres. In doing…
The Yrast Line of a Rapidly Rotating Bose Gas: Gross-Pitaevskii Regime
Elliott H. Lieb, Robert Seiringer, Jakob Yngvason
We consider an ultracold rotating Bose gas in a harmonic trap close to the critical angular velocity so that the system can be considered to be confined to the lowest Landau level.…
Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices
Eric A. Carlen, Elliott H. Lieb
A theorem of Mirsky provides necessary and sufficient conditions for the existence of an N-square complex matrix with prescribed diagonal entries and prescribed eigenvalues. We giv…