Quadratic estimates for Hodge-Dirac operators with potentials

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• Andrew J. Morris (University of Birmingham)
• Monday 28 September 2015, 16:00-17:00
• Lecture Theatre 4, Strathcona Building.

If you have a question about this talk, please contact Alessio Martini.

We prove quadratic estimates for additive perturbations of first-order elliptic systems on Rⁿ, such as the perturbed Hodge-Dirac operator D=d+d*+V. In particular, homogeneous estimates require potentials V in Lⁿ with sufficiently small norm. A substantial reworking of existing techniques is needed in that case. The inhomogeneous estimates, however, follow from a straight-forward perturbation argument that allows for potentials V in L^p for any p>n. The solution of the Kato square root problem for second-order elliptic equations with singular lower order terms follows as an application. This includes magnetic Schrödinger operators with singular potentials.

This talk is part of the Analysis seminar series.

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• Analysis seminar
• Lecture Theatre 4, Strathcona Building
• School of Mathematics events

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