17 citations · 51 across the 14 of their papers we have counts for
5 papers · 1 filter
Characterization of the critical magnetic field in the Dirac-Coulomb equation
Jean Dolbeault, Maria J. Esteban, Michael Loss
We consider a relativistic hydrogenic atom in a strong magnetic field. The ground state level depends on the strength of the magnetic field and reaches the lower end of the spectra…
Stability of atoms and molecules in an ultrarelativistic Thomas-Fermi-Weizsaecker model
Rafael D. Benguria, Michael Loss, Heinz Siedentop
We consider the zero mass limit of a relativistic Thomas-Fermi-Weizsaecker model of atoms and molecules. We find bounds for the critical nuclear charges that ensure stability.
Polya's conjecture in the presence of a constant magnetic field
Rupert L. Frank, Michael Loss, Timo Weidl
We consider the Dirichlet Laplacian with a constant magnetic field in a two-dimensional domain of finite measure. We determine the sharp constants in semi-classical eigenvalue esti…
Determination of the spectral gap in the Kac model for physical momentum and energy conserving collisions
Eric A. Carlen, Jeffry S. Geronimo, Michael Loss
The Kac model describes the local evolution of a gas of particles with three dimensional velocities by a random walk in which the steps correspond to binary collisions that con…
The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space
Rafael D. Benguria, Rupert L. Frank, Michael Loss
It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the three dimensional upper half space is given by the Sobolev constant. This is achieved by a duality…