The analysis of eigenvalues of Laplace and Schrödinger operators is an important and
classical topic in mathematical physics with many applications. This book presents a …

This survey is dedicated to the 100th anniversary of Mark Iosifovich Vishik and is based on a
number of mini-courses taught by the author at University of Surrey (UK) and Lanzhou …

arxiv:2007.09326v1 [math-ph] 18 Jul 2020 Page 1 arxiv:2007.09326v1 [math-ph] 18 Jul 2020
THE LIEB–THIRRING INEQUALITIES: RECENT RESULTS AND OPEN PROBLEMS RUPERT …

We explore a variety of unsolved problems in density functional theory, where
mathematicians might prove useful. We give the background and context of the different …

In this chapter we first review the Levy–Lieb functional, which gives the lowest kinetic and
interaction energy that can be reached with all possible quantum states having a given …

There are several proofs by now for the famous Cwikel–Lieb–Rozenblum (CLR) bound,
which is a semiclassical bound on the number of bound states for a Schrödinger operator …

Given 0< s< d 2 with s Ä 1, we are interested in the large N-behavior of the optimal constant
ÄN in the Hardy inequality Pn nD1. n/s ÄN P n< m jXn Xmj 2s, when restricted to …

We study the nonlinear Schrödinger equation for systems of N orthonormal functions. We
prove the existence of ground states for all N when the exponent p of the non linearity is not …

We study ground states of a relativistic Fermi system involved with the pseudo-differential
operator-c 2 Δ+ c 4 m 2-c 2 m in the L 2-subcritical case, where m> 0 denotes the rest mass …

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 …