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math.AP2020★ 15 cited
The nonlinear Schrödinger equation for orthonormal functions: II. Application to Lieb-Thirring inequalities
Rupert L. Frank, David Gontier, Mathieu Lewin
In this paper we disprove part of a conjecture of Lieb and Thirring concerning the best constant in their eponymous inequality. We prove that the best Lieb-Thirring constant when t…
math.AP2020★ 14 cited
The nonlinear Schrödinger equation for orthonormal functions: I. Existence of ground states
David Gontier, Mathieu Lewin, Faizan Q. Nazar
We study the nonlinear Schrödinger equation for systems of orthonormal functions. We prove the existence of ground states for all when the exponent of the non linearity…