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Graduate Student Analysis Seminar

Best representative of Sobolev functions

Zhuolun Yang, Rutgers University

Location:  Hill GSL
Date & time: Monday, 16 October 2017 at 5:00PM - 6:00PM

  Abstract:  Given a Lebegue integrable function, if we take its average on a ball and shrink the radius to 0, we know the limit exists almost everywhere by Lebesgue differential theorem. This limit gives us a good representative for Lebegue integrable. What if we know its derivatives are also integrable? Should we expect the “singular set” to be smaller? In this talk, I will introduce Capacity measure to measure this “singular set” of Sobolev functions. I will go over some classical arguments in measure theory, and some of which are very useful for PDE. e.g. to get partial regularity.

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
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