32 citations · 65 across the 8 of their papers we have counts for
5 papers · 1 filter
Spectral inequalities for Schroedinger operators with surface potentials
Rupert L. Frank, Ari Laptev
We prove sharp Lieb-Thirring inequalities for Schroedinger operators with potentials supported on a hyperplane and we show how these estimates are related to Lieb-Thirring inequali…
Eigenvalue estimates for the Aharonov-Bohm operator in a domain
Rupert L. Frank, Anders Hansson
We prove semi-classical estimates on moments of eigenvalues of the Aharonov-Bohm operator in bounded two-dimensional domains. Moreover, we present a counterexample to the generaliz…
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…
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…
The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction
Rupert L. Frank, Heinz Siedentop, Simone Warzel
We describe atoms by a pseudo-relativistic model that has its origin in the work of Chandrasekhar. We prove that the leading energy correction for heavy atoms, the Scott correction…