32 citations · 65 across the 8 of their papers we have counts for
8 papers
Non-linear ground state representations and sharp Hardy inequalities
Rupert L. Frank, Robert Seiringer
We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, w…
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…
Eigenvalue estimates for magnetic Schroedinger operators in domains
Rupert L. Frank, Ari Laptev, Stanislav Molchanov
Inequalities are derived for sums and quotients of eigenvalues of magnetic Schroedinger operators with non-negative electric potentials in domains. The bounds reflect the correct o…
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…