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Conference on "Mathematical properties of large quantum systems"
Organizers: Maria J. Esteban (CNRS), Mathieu Lewin (CNRS), Robert Seiringer (McGill, Montréal) & Jan Philip Solovej (Copenhagen)


Enno Lenzmann (Basel, Switzerland): "Theorems of ODE type for the fractional Laplacian"
Thursday 20 June 2013, 11:50 - 12:35
Amphi Hermite


In this talk, I will survey recent joint work with Rupert Frank and Luis Silvestre on linear and nonlinear problems involving the fractional Laplacian. In particular, I will discuss how to obtain ODE-type theorems about uniqueness and oscillation for radial solutions of equations with the fractional Laplacian in all space dimensions. By a novel monotonicity formula for harmonic functions, we show simplicity of all radial eigenvalues for fractional Schrödinger operators with increasing potentials. As an application, we prove uniqueness (modulo symmetries) of optimizers for the fractional Gagliardo-Nirenberg-Sobolev inequality.

Although this talk centers on PDE questions, I will (try to) provide a sufficient amount of physical motivation along the way.