539 citations · 6.8k across the 160 of their papers we have counts for
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Stability estimate for the Lane-Emden inequality
Eric Carlen, Mathieu Lewin, Elliott H. Lieb +1
The Lane-Emden inequality controls in terms of the and norms of . We provide a remainder estimate for this inequa…
A note on a theorem of M. Christ
Rupert L. Frank, Elliott H. Lieb
This note is a supplement to our paper `Proof of spherical flocking based on quantitative rearrangement inequalities'. Recently, M. Christ has derived a deep result concerning stab…
Proof of spherical flocking based on quantitative rearrangement inequalities
Rupert L. Frank, Elliott H. Lieb
Our recent work on the Burchard-Choksi-Topaloglu flocking problem showed that in the large mass regime the ground state density profile is the characteristic function of some set.…
A `liquid-solid' phase transition in a simple model for swarming, based on the `no flat-spots' theorem for subharmonic functions
Rupert L. Frank, Elliott H. Lieb
We consider a non-local shape optimization problem, which is motivated by a simple model for swarming and other self-assembly/aggregation models, and prove the existence of differe…
Strichartz inequality for orthonormal functions
Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb +1
We prove a Strichartz inequality for a system of orthonormal functions, with an optimal behavior of the constant in the limit of a large number of functions. The estimate generaliz…
Stability estimates for the lowest eigenvalue of a Schrödinger operator
Eric A. Carlen, Rupert L. Frank, Elliott H. Lieb
There is a family of potentials that minimize the lowest eigenvalue of a Schrödinger eigenvalue under the constraint of a given L^p norm of the potential. We give effective estimat…
Sharp constants in several inequalities on the Heisenberg group
Rupert L. Frank, Elliott H. Lieb
We derive the sharp constants for the inequalities on the Heisenberg group H^n whose analogues on Euclidean space R^n are the well known Hardy-Littlewood-Sobolev inequalities. Only…