The presentations will be held in the last two weeks of classes.

Schedule

  1. Mon, Apr 17: Seongmin Jeon, Proof of “Filling holes” estimate
  2. Wed, Apr 19: Yuqing Li, Schaeffer’s example of singular points
  3. Fri, Apr 21: Zachary Selk, Andersson-Weiss counterexample
  4. Mon, Apr 24: Hengrong Du, Friedland-Hayman Inequality
  5. Wed, Apr 26: Ziyao Yu, Up to boundary *C1,1 regularity*
  6. Fri, Apr 28: Qinfeng Li, Uniqueness of blowups using Epiperimetric inequality

Topics for Presentations

  1. Proof of “Filling holes” estimate, [PSU, Lemma 9.1 and Exercise 9.3]
  2. Schaeffer’s example of singular points, [PSU, §7.3 and Exercise 7.2]
  3. Andersson-Weiss counterexample, [PSU, §2.5 and Exercise 2.8]
  4. Friedland-Hayman Inequality, from [CS, §12.3]
  5. Up to boundary C1,1 regularity [PSU, §2.4]
  6. Uniqueness of blowups using Epiperimetric inequality, [Wei, §6]

References

[CS] L. Caffarelli, S. Salsa, A geometric approach to free boundary problems, Graduate Studies in Mathematics 68, American Mathematical Society, Providence, RI, 2005
[PSU] A. Petrosyan, H. Shahgholian, N. Uraltseva, Regularity of free boundaries in obstacle-type problems, Graduate Studies in Mathematics 136, American Mathematical Society, Providence, RI, 2012
[Wei] G.S. Weiss, A homogeneity improvement approach to the obstacle problem, Invent. Math. 138 (1999), no. 1, 23–50