Solution operators for divergence-type equations with prescribed support properties

The HADES seminar on Tuesday, November 2nd, will be given by Sung-Jin Oh at 5 pm in 740 Evans.

Speaker: Sung-Jin Oh

Abstract: An alternative title for this talk could be “What I wish I knew about the divergence equation in graduate school.” Equations that resemble the prescribed divergence equation arise from many places in physics, such as the incompressibility condition in fluid mechanics, the Gauss law in electromagnetism and the (linearized) constraint equations in general relativity. I will describe a construction of solution operators for these equations with certain support properties based on a few simple ideas, such as manipulation of delta distributions, smooth averaging and standard harmonic analysis. Then I will discuss how such a construction leads to simplification (and improvement) of some theorems for the Yang-Mills and Einstein equations.

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