56 citations · 259 across the 34 of their papers we have counts for
9 papers · 1 filter
Existence and non-existence of minimizers for a multi-particle model with concave nonlinearity
David Gontier, Salma Lahbabi, Simona Rota Nodari
We study a multi--particle model including a kinetic energy and a non linear local self-interaction, both in the bosonic and fermionic cases. In both cases, we prove that the model…
Keller and Lieb-Thirring estimates of the eigenvalues in the gap of Dirac operators
Jean Dolbeault, David Gontier, Fabio Pizzichillo +1
We estimate the lowest eigenvalue in the gap of the essential spectrum of a Dirac operator with mass in terms of a Lebesgue norm of the potential. Such a bound is the counterpart f…
Optimizers for the finite-rank Lieb-Thirring inequality
Rupert L. Frank, David Gontier, Mathieu Lewin
The finite-rank Lieb-Thirring inequality provides an estimate on a Riesz sum of the lowest eigenvalues of a Schrödinger operator in terms of an no…
Edge states for second order elliptic operators in a channel
David Gontier
We present a general framework to study edge states for second order elliptic operators in a half channel. We associate an integer valued index to some bulk materials, and we prove…
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…
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…
Sub-wavelength focusing of acoustic waves in bubbly media
Habib Ammari, Brian Fitzpatrick, David Gontier +2
The purpose of this paper is to investigate acoustic wave scattering by a large number of bubbles in a liquid at frequencies near the Minnaert resonance frequency. This bubbly medi…
A mathematical and numerical framework for bubble meta-screens
Habib Ammari, Brian Fitzpatrick, David Gontier +2
The aim of this paper is to provide a mathematical and numerical framework for the analysis and design of bubble meta-screens. An acoustic meta-screen is a thin sheet with patterne…
Minnaert resonances for acoustic waves in bubbly media
Habib Ammari, Brian Fitzpatrick, David Gontier +2
Through the application of layer potential techniques and Gohberg-Sigal theory we derive an original formula for the Minnaert resonance frequencies of arbitrarily shaped bubbles. W…