Keller estimates of the eigenvalues in the gap of Dirac operators

Abstract: The Keller inequality is the Lp version of the well-known Lord Rayleygh problem: "What shape of drum produces the lowest note?”, but this time, the drum is a potential with fixed Lp norm. In the usual Schrödinger case, was solved by Faber and Krahn around 1920, and turns out to be equivalent to the Gagliardo-Niremberg inequality. However, the usual techniques do not apply to the Dirac case. In this talk, I will provide a novel technique which allows to tackle the problem both for Schrödinger and Dirac operators, and which provides interesting numerical schemes for this optimization problem. I will mention several open problems related to the Dirac case.

mathematical physics

Audience: researchers in the discipline

One world IAMP mathematical physics seminar

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